DRAFTVERSION OCTOBER 2, 2018 Typeset using LATEX twocolumn style in AASTeX61

ULTRA-WIDEBAND DETECTION OF 22 COHERENT RADIO BURSTS ON M DWARFS

∗ JACKIE VILLADSEN1, 2 , AND GREGG HALLINAN2

1National Radio Astronomy Observatory 520 Edgemont Rd Charlottesville, VA 22903 2California Institute of Technology 1200 E California Blvd, MC 249-17 Pasadena, CA 91125

ABSTRACT Coherent radio bursts detected from M dwarfs have some analogy with solar radio bursts, but reach orders of magnitude higher luminosities. These events trace particle acceleration, powered by magnetic reconnection, shock fronts (such as formed by coronal mass ejections, CMEs), and magnetospheric currents, in some cases offering the only window into these processes in stellar atmospheres. We conducted a 58-hour, ultra-wideband survey for coherent radio bursts on 5 active M dwarfs. We used the Karl G. Jansky Very Large Array (VLA) to observe simultaneously in three frequency bands covering a subset of 224- 482 MHz and 1-6 GHz, achieving the widest fractional bandwidth to date for any observations of stellar radio bursts. We detected 22 bursts across 13 epochs, providing the first large sample of wideband dynamic spectra of stellar coherent radio bursts. The observed bursts have diverse morphology, with durations ranging from seconds to hours, but all share strong (40-100%) circular polarization. No events resemble solar Type II bursts (often associated with CMEs), but we cannot rule out the occurrence of radio-quiet stellar CMEs. The hours-long bursts are all polarized in the sense of the x-mode of the star’s large-scale magnetic field, suggesting they are cyclotron maser emission from electrons accelerated in the large-scale field, analogous to auroral processes on ultracool dwarfs. The duty cycle of luminous coherent bursts peaks at 25% at 1-1.4 GHz, declining at lower and higher frequencies, indicating source regions in the low corona. At these frequencies, active M dwarfs should be the most common galactic transient source.

Keywords: stars: flare — stars: coronae — radio continuum: stars arXiv:1810.00855v1 [astro-ph.SR] 1 Oct 2018

Corresponding author: Jackie Villadsen [email protected], [email protected] ∗ Jackie Villadsen is a Jansky Fellow of the National Radio Astronomy Observatory. 2 VILLADSENETAL.

1. INTRODUCTION ations of exoplanet habitability (Shields et al. 2016). In con- The Sun produces intense bursts of emission at low ra- trast to solar-type stars, M dwarfs retain their youthful rapid dio frequencies, which caused it to become the second de- rotation (Newton et al. 2016) and vigorous magnetic activ- tected astrophysical radio source after the Galactic center ity (West et al. 2008) for hundreds of millions to billions of (Hey 1946; Southworth 1945; Orchiston 2005). These bursts years. Even old, slowly rotating M dwarfs can have signifi- are classified according to their morphology in the time- cant magnetic spot coverage (Newton et al. 2016) and pow- frequency plane (“dynamic spectrum”), reviewed in Dulk erful flares (France et al. 2016). Active M dwarfs have a high (1985) and Bastian et al.(1998). There are a large num- rate of energetic flares (Lacy et al. 1976), with potentially ber of types of solar radio bursts, with durations from mil- dramatic consequences for planetary atmospheres: coronal liseconds to weeks, at frequencies from kHz to GHz. Many mass ejections can compress the planetary magnetosphere of the bursts have high brightness temperatures, strong cir- and erode the atmosphere (Khodachenko et al. 2007; Lam- cular polarization, and/or narrow bandwidth, indicating that mer et al. 2007; Kay et al. 2016; Patsourakos & Georgoulis they are powered by coherent emission mechanisms, plasma 2017) and stellar energetic particles can penetrate deep into emission or electron cyclotron maser (ECM) emission. As a the atmosphere and interact chemically (Segura et al. 2010; picture has emerged for the origin of the different types of Airapetian et al. 2016; Tilley et al. 2017; Howard et al. 2018). bursts, they have proved to have significant diagnostic power There is limited observational evidence of CMEs and ener- for processes in the solar corona and interplanetary medium, getic protons around stars other than the Sun, so models of including Earth-impacting (“geoeffective”) events. the impact of stellar ejecta on exoplanetary atmospheres must Two tracers of geoeffective space weather events are solar rely on extrapolating solar relationships, between flares and Type II and Type III bursts, which occur at frequencies from CMEs (Yashiro & Gopalswamy 2009; Aarnio et al. 2011; hundreds of MHz down to kHz. These bursts occur at the Drake et al. 2013; Osten & Wolk 2015; Odert et al. 2017), local plasma frequency and its second harmonic, and their magnetic flux and CMEs (Cranmer 2017), and flares and en- frequency declines over time as a coronal source moves out- ergetic protons (Belov et al. 2007; Cliver et al. 2012; Atri wards into lower densities. Solar Type II bursts trace coronal 2017; Youngblood et al. 2017), to apply to the high-energy shock fronts, moving at speeds of order 1000 km s−1, passing flares and strongly magnetized coronae of active M dwarfs. through a decade in plasma frequency in a matter of min- There are both observational and theoretical reasons to ex- utes. These shocks may be driven by coronal mass ejections pect that solar scaling relationships for CMEs and energetic (CMEs) or by flare blast waves (Vršnak & Cliver 2008). So- protons may not apply to active M dwarfs. Observations of lar Type III bursts are produced by electron beams moving Lyman α absorption in the astrosphere of active M dwarf at speeds of order 10% of the speed of light, with radio fre- EV Lac indicate that it has a mass loss rate similar to the Sun quency decreasing exponentially on a timescale of seconds; (assuming isotropic mass loss; Wood et al. 2005), in contrast when these bursts occur at low frequencies, they indicate that to the flare-based prediction of Osten & Wolk(2015) that it energetic electrons (and likely protons as well) are escap- would be up to 500 times greater due to frequent CMEs. The ing the solar corona on open magnetic field lines. Both of strong global field of active M dwarfs (kG strength - Morin these classes of bursts are correlated with solar space weather et al. 2008) may confine or prevent eruptions (Vidotto et al. events that impact Earth: coronal mass ejections and solar 2016; Odert et al. 2017; Alvarado-Gómez et al. 2018), as energetic particle (SEP) events (Kouloumvakos et al. 2015). has been suggested for the few strong solar flares that are Analogous events, tracing bulk motion of plasma, may be de- not accompanied by CMEs (Thalmann et al. 2015; Sun et al. tectable from nearby stars; and based on Sun-as-a-star data, 2015). In addition, the most intense solar energetic parti- such stellar radio bursts can be used to recover approximate cle events that hit Earth are caused by particle acceleration dynamical properties of CMEs (Crosley et al. 2017). This at CME shocks (Reames 2013), so solar flare-proton scaling suggests that low-frequency radio observations can be used relationships will not apply well to active stars if energetic to characterize stellar mass loss and the space weather envi- flares are not accompanied by CMEs or if those CMEs do ronment experienced by extrasolar planets. not form shocks to accelerate particles; shocks may be rare Based on planet occurrence statistics, many of the near- due to high Alfvén speeds in the strongly magnetized stel- est habitable-zone Earth-size planets should be found around lar coronae. With all these complicating factors, there is a M dwarfs (Dressing & Charbonneau 2015), a prediction need for direct stellar observations to test for the presence of borne out by the planet detections around Proxima Cen CMEs, shocks, and energetic particles. (Anglada-Escudé et al. 2016), TRAPPIST-1 (Gillon et al. Beyond radio observations, various other observational 2017), and Ross 128 (Bonfils et al. 2017). However, the techniques provide evidence suggestive of stellar erup- space weather environment around M dwarfs may differ dra- tions. Chromospheric and coronal emission lines some- matically from our own solar system, complicating consider- times display blueshifted emission components during flares COHERENT RADIO BURSTSON MDWARFS 3 on M dwarfs (e.g., Houdebine et al. 1990; Fuhrmeister & II and III radio bursts) have been inconclusive: while early Schmitt 2004; Leitzinger et al. 2011; Vida et al. 2016). Sur- observations yielded bright events coincident with optical veys with many hours of stellar observations (Leitzinger flares (e.g., Lovell 1963), these events may have been due et al. 2014; Vida et al. 2016) have detected these blueshifted to RFI. Later experiments imposed additional requirements features at a rate much lower than the rate of energetic flares, to distinguish between stellar bursts and RFI, including: in- but Leitzinger et al.(2014) attribute this low rate of CME terferometric observations (finding two hours-long 408-MHz detections to sensitivity limits. bursts on YZ CMi; Davis et al. 1978), absence of the sig- Harra et al.(2016) searched for ways of differentiating be- nal in off-source beams (identifying a handful of candidate tween eruptive and non-eruptive energetic solar flares, using events; e.g., Abdul-Aziz et al. 1995; Abranin et al. 1998), optical, EUV, and X-ray signatures potentially observable in and spectral shape of the burst (yielding a short 430-MHz stars. They ruled out long flare decay timescales (suggested burst on YZ CMi; Bastian et al. 1990). Other low-frequency as evidence of a stellar eruption on AU Mic; Cully et al. 1994; observations produced marginal or uncertain detections (e.g., Katsova et al. 1999) and identified only one reliable indicator Jackson et al. 1990). Recent Low-Frequency Array (LO- of eruptive flares: coronal dimming, when coronal EUV line FAR) beam-formed observations of YZ CMi at 10-190 MHz emission decreases as a CME carries away coronal material yielded no detections (Crosley et al. 2016), while Lynch et al. (detectable in Sun-as-a-star observations; Mason et al. 2014). (2017) detected multiple 154-MHz bursts on UV Cet using The closest stellar analog to this so far is a post-flare reduc- interferometric imaging with the Murchison Widefield Ar- tion in EUV continuum and transition region line emission ray (MWA). VLA observations of EQ Peg at 230-470 MHz on active M dwarf EV Lac (Ambruster et al. 1986). Stel- detected two coherent bursts (Crosley & Osten 2018b), but lar eruptions have also been invoked to explain diverse cases no Type II-like events in spite of an optical flare rate imply- of absorption of stellar chromospheric line emission (Collier ing that this star may produce CMEs at least once per hour Cameron & Robinson 1989; Bond et al. 2001) and coronal X- (Crosley & Osten 2018a). ray continuum (Haisch et al. 1983; Favata & Schmitt 1999). While many observational methods provide hints of stel- Another observational signature of CMEs may be their im- lar eruptions, none so far have yielded unequivocal evidence pact on the circumstellar environment. CMEs have been pro- of an eruption nor a systematic collection of candidate CME posed as drivers of observed variability in a hot Jupiter atmo- events. This is due to limitations on sensitivity, wavelength sphere (Lecavelier des Etangs et al. 2012) and circumstellar range, and/or available observing time of existing facilities, disks (Osten et al. 2013; Boccaletti et al. 2015). as well as the possibility that M dwarfs do not produce CMEs Finally, wideband radio spectroscopy of stellar coherent according to the solar paradigm. Recent and upcoming im- radio bursts can track outwards-moving coronal sources, of- provements in radio facilities mean that radio observations fering the potential for direct observations of stellar erup- may now be able to detect a population of stellar space tions. Coherent radio bursts are abundant on active M dwarfs, weather events. dominating the population of radio flares observed on these The recently upgraded Karl G. Jansky Very Large Array stars below 5 GHz (Bastian 1990). However, given the strong (VLA) offers wide instantaneous bandwidth and low observ- global magnetic field and rapid rotation of active M dwarfs, it ing frequencies, making it a powerful instrument for search- is not clear whether these bursts can be interpreted within the ing for stellar eruptions. We have conducted a 58-hour sur- solar paradigm. Dynamic spectroscopy has helped to charac- vey of a sample of 5 active M dwarfs with the VLA, using terize these bursts, finding features such as striae with rapid the VLA’s subarray capabilities to achieve ultra-wide band- frequency drift (Osten & Bastian 2008), rapid time variabil- width over a subset of frequencies from 224-482 MHz and ity, and strong circular polarization that provide evidence that 1-6 GHz. We analyze the results of this survey in a series of ECM may be responsible for many of these bursts. A num- three papers. In this paper (Paper I), we present the ensemble ber of coherent radio bursts in stellar atmospheres are also of coherent radio bursts detected by the survey, consider the attributed to plasma emission (Stepanov et al. 2001; Osten physical origins of two populations of events (short-duration & Bastian 2006), a promising sign that events analogous to bursts and long-duration bursts), and predict rates of stellar the solar Type II and Type III plasma-frequency bursts may coherent radio bursts for upcoming transient surveys. Pa- occur in stellar atmospheres. In particular, Osten & Bastian pers II and III analyze in detail a series of coherent bursts on (2006) detected a 1.4-GHz burst on AD Leo with gradual fre- UV Cet and AD Leo, respectively, accompanied by simul- quency drift that may correspond to a disturbance in the low taneous 8.2-8.5 GHz high-resolution imaging with the Very corona moving outwards at speeds of 1200-12000 km s−1, as Long Baseline Array (VLBA). expected for a CME or a flare blast wave. Searches for stellar coherent radio bursts at low frequen- cies (<1 GHz, the frequency range for observing solar Type 2. OBSERVATIONS 4 VILLADSENETAL.

Table 1. Summary of Observations.

Star Date Duration (hrs) Frequency (GHz) Flux Calibrator Gain Calibrator VLA Configuration

AD Leo 2013 Apr 24 2 2-6a 3C147 J1111+1955 D 2013 May 26 2 1-6 3C147 J1111+1955 DnC 2013 Jun 2 2 1-6 3C147 J1111+1955 DnC→C 2013 Jul 27 2 1-6 3C147 J1111+1955 C 2015 May 12 2 0.22-0.48, 1-4 3C286 J1111+1955 B→BnA 2015 May 13 2 0.22-0.48, 1-4 3C286 J1111+1955 B→BnA 2015 Jul 5 4 0.22-0.48, 1-4b 3C286 J1111+1955 A 2015 Jul 19 4 0.22-0.48, 1-4b 3C286 J1111+1955 A 2015 Sep 5 4 0.22-0.48, 1-4b 3C286 J1111+1955 A

UV Cet 2013 May 26 2 1-6 3C48 J0204-1701 DnC 2013 Jun 2 2 1-6 3C48 J0204-1701 DnC→C 2013 Aug 24 2 1-6 3C48 J0204-1701 C 2015 May 15 2 1-2a 3C147 J0204-1701 B→BnA 2015 May 16 2 0.22-0.48, 1-4 3C147 J0204-1701 B→BnA 2015 Jul 4 4 0.22-0.48, 1-4b 3C147 J0204-1701 A 2015 Jul 18 4 0.22-0.48, 1-4b 3C147 J0204-1701 A 2015 Sep 6 4 0.22-0.48, 1-4b 3C147 J0204-1701 A

EQ Peg 2015 May 15 2 0.22-0.48, 1-4 3C147 J2254+2445 B→BnA 2015 May 16 2 0.22-0.48, 1-4 3C147 J2254+2445 B→BnA

EV Lac 2015 May 12 2 0.22-0.48, 1-4 3C286 J2202+4216 B→BnA 2015 May 13 2 0.22-0.48, 1-4 3C286 J2202+4216 B→BnA

YZ CMi 2015 May 11 2 0.22-0.48, 1-4 3C147 J0745+1011 B→BnA 2015 May 13 2 0.22-0.48, 1-4 3C147 J0745+1011 B→BnA

aNarrower bandwidth is due to bad data in some bands during these observations. bThe 4-hour blocks have simultaneous VLBA observations at 8.2-8.5 GHz.

The survey consists of 58 hours of VLA observations in The targets are main sequence stars whose rapid rotation 2013 and 2015, summarized in Table1. The observations rates (Table2) suggest an age less than ∼2 Gyr (Newton et al. consist of 2- and 4-hour observing blocks on individual tar- 2016). To the best of our knowledge, these stars do not show gets (these durations include 20-25% overhead time on cali- indicators of extreme youth such as low surface gravity or brators), for a total of 14 hours in 2013 observing two targets lithium (ruled out for EV Lac by Shkolnik et al. 2009). These at 1-6 GHz, and 44 hours in 2015 observing five targets at stars represent an early evolutionary stage that many mid- 0.22-0.48 and 1-4 GHz. M dwarfs should inhabit for hundreds of millions of years, affecting the long-term evolution of planetary atmospheres. 2.1. Target Stars The targets produce a high rate of energetic flares across 34 The targets are well-known flare stars of spectral type the electromagnetic spectrum, including > 10 -erg super- M3.5V to M6V, summarized in Table2: AD Leonis, binary flares on AD Leo (Hawley & Pettersen 1991) and YZ CMi BL & UV Ceti (semi-major axis 2.1”; Kervella et al. 2016), (Kowalski et al. 2010) that likely occur about once a month. binary EQ Pegasi AB (semi-major axis 6.9”; Heintz 1984), Lacy et al.(1976) measured optical U-band flare frequency EV Lacertae, and YZ Canis Minoris. Both binaries are un- distributions for all of our targets, finding that the stars pro- 30 resolved by most of the VLA observations; in this paper the duce flares with U-band energy EU > 5 × 10 erg every ∼1- names “UV Cet” and “EQ Peg” refer to the binary systems 15 hours (depending on which star). This corresponds to a 31 unless otherwise specified. bolometric flare energy of ∼ 5 × 10 erg (Osten & Wolk COHERENT RADIO BURSTSON MDWARFS 5

2015), above which 100% of solar flares are associated with vious detections of stellar radio bursts have achieved con- CMEs (Yashiro et al. 2006; Osten & Wolk 2015). Crosley tinuous frequency coverage of νmax/νmin up to 1.4 (Osten & et al.(2016) use solar flare-CME scaling relationships to pre- Bastian 2008) or have observed widely spaced narrow bands 30 dict that EU ∼ 2 × 10 erg is the minimum flare energy for (e.g., Spangler & Moffett 1976). In contrast, solar spectro- an associated CME to form a shock (a necessary condition graphs offer continuous frequency coverage for νmax/νmin of to produce a Type II burst) at a height of 2R∗ in a simple 10 to 100, with facilities such as the 10-1000 MHz Green coronal model of YZ CMi. Thus if these stars follow so- Bank Solar Radio Burst Spectrometer and the 18-1800 MHz lar flare-CME scaling relationships, they may produce super- Culgoora Solar Radio Spectrograph. Our survey increases Alfvénic (shock-forming) CMEs every few hours. However, the fractional bandwidth achieved for stellar observations, as discussed in Section1, there is a gap in understanding as to with continuous frequency coverage over νmax/νmin of 6 (1-6 how the extreme coronal conditions of these stars impact the GHz) in 2013 and partial frequency coverage over νmax/νmin relationship between flares and CMEs. Notably, Alvarado- of 18 (0.22-0.48 and 1-4 GHz) in 2015. To achieve this wide Gómez et al.(2018) predict that strong global magnetic fields bandwidth, we divided the VLA into three subarrays to ob- may suppress CMEs for bolometric flare energies less than serve three frequency bands simultaneously; the upgraded 6 × 1032 erg, and reduce the velocity of even the more ener- VLA’s wideband feeds and WIDAR correlator enabled up getic CMEs, potentially preventing shock formation. to 2 GHz bandwidth in each band. The 2013 observations The high rate of magnetic energy release in the outer at- cover L band (1-2 GHz, 1 MHz channels), S band (2-4 GHz, mospheres of these stars powers coronae that are both hot- 2 MHz channels) and C band (4-6 GHz, 2 MHz channels), ter and denser than the Sun’s (Table2). X-ray observations with 9 antennas per subarray. The 2015 observations cover show the targets have quiescent coronal temperatures of ∼3- P band (224-482 MHz, 125 kHz channels) with 15 antennas 10 MK, in contrast to the Sun’s 1-3 MK, and electron den- to compensate for its lower sensitivity, and L and S bands sities about 100 times greater than in the Sun’s corona. The with 6 antennas each (the achieved sensitivities are given in stars also have large-scale magnetic fields very different from Section 3.2). This enables the detection of features in the the Sun’s, thanks to their rapid rotation and fully convective dynamic spectrum across a much wider bandwidth, with two dynamo. While photospheric magnetic field strengths in ac- benefits: 1) increased probability of detecting narrowband tive regions saturate at kilo-Gauss levels in both the Sun and bursts; and 2) the potential to track coronal sources as they active M dwarfs, the covering fraction of these fields is much propagate across 1-2 orders of magnitude in coronal density larger for active M dwarfs, about 50-100% (Shulyak et al. or magnetic field strength, corresponding to a wide range of 2014), compared to ∼1% for the Sun. A significant fraction heights above the star. of the target stars’ magnetic flux is in the large-scale field This survey targets relatively high frequencies compared (Reiners & Basri 2009). Morin et al.(2008) and Kochukhov to the distribution of CME-associated solar Type II bursts. & Lavail(2017) have mapped the large-scale magnetic field Solar Type II radio bursts, which originate from shock fronts of all the target stars, finding that the large-scale components in the corona or interplanetary medium, are detected at of the field (dipole, quadrupole, ...) have a combined strength 100s of MHz and below (start frequency distributions in, of hundreds of Gauss to a few kilo-Gauss, in contrast to a few e.g., Roberts 1959; Prakash et al. 2010), but only rarely at Gauss on the Sun (Vidotto et al. 2016). the highest frequencies of ∼100-600 MHz. The highest- The observed stars are known to produce broadband frequency Type II bursts, originating low in the solar corona, slowly-variable quiescent emission, attributed to incoher- are sometimes associated with CME-driven shocks (Cho ent non-thermal gyrosynchrotron radiation, with flares on et al. 2013; Kouloumvakos et al. 2015; Kumari et al. 2017), timescales of minutes to days (reviews: Bastian 1990; Güdel but can also be caused without a CME due to coronal shocks 2002). While the observed data set could also be used to driven by blast waves from flare sites (Vršnak & Cliver 2008; study incoherent radio emission from flares, this paper fo- Magdalenic´ et al. 2012) or by rapidly expanding magnetic cuses instead on the search for coherent radio bursts, where structures (Su et al. 2015). In contrast, all Type II bursts the signature of coherent processes is seen in narrow band- at low frequencies (<1 MHz) are attributed to CME-driven widths or complex spectral structure, rapid time variability shocks (Cane et al. 1987). However, geoeffective CMEs and high flux densities implying high brightness tempera- that cause solar energetic particle (SEP) events tend to form tures, and strong circular polarization of up to 100%. shocks relatively low in the corona, producing Type II bursts that start at high frequencies (Prakash et al. 2017). 2.2. Choice of Frequency Bands Active M dwarfs have high coronal densities compared to the Sun, making it plausible to observe coronal plasma emis- A key feature of this survey is its extremely wide fractional sion at higher frequencies. Table2 lists coronal electron den- bandwidth, defined here as ν /ν , the ratio of highest fre- max min sities for these stars based on OVII line ratios, which are most quency to lowest frequency observed simultaneously. Pre- 6 VILLADSENETAL.

Table 2. Properties of Target Stars.

Observed properties Hydrostatic equilibrium model

Star Spectral Type Distance Prot Mass Radius Tcor log ne Density scale height νp at r = 2R∗ −3 pc days M R MK cm Mm R∗ MHz AD Leo M3V 4.7 2.24 0.42 0.44 2-10 10.4 115 0.38 420 EQ Peg A M3.5V 6.2 1.06 0.39 0.41 ∼3 10.6 62 0.29 280 EQ Peg B M4.5V 0.40 0.25 0.30 ∼3 <11.0 90 0.43 500 EV Lac M3.5V 5.1 4.38 0.32 0.30 2-10 10.3-10.7 70 0.34 360 YZ CMi M4V 6.0 2.78 0.31 0.29 4-7 10.5 68 0.34 360 BL Cet M5.5V 2.7 0.24 0.12 0.17 3-6 ··· 60 0.51 600 UV Cet M6V 0.23 0.12 0.16 3-6 ··· 53 0.48 560 Sun G2V ∼25 1 1 1-3 8.5 100 0.14 5

NOTE—Solar properties are shown for comparison. The hydrostatic equilibrium model, discussed in Section 2.2, assumes a coronal temperature of 5 MK for the stars and 2 MK for the Sun, and a coronal base density (log ne) of 10.5 for the stars and 8.5 for the Sun, corresponding to a plasma frequency of 1.6 GHz at the base of the stellar coronae and 160 MHz at the base of the solar corona. References— Spectral type: Henry et al.(1994). Distance: SIMBAD database. Rotation period: AD Leo, EQ Peg A/B, EV Lac, YZ CMi - Morin et al.(2008). BL Cet, UV Cet - Barnes et al.(2017). Mass: AD Leo, EQ Peg A/B, EV Lac, YZ CMi - photometric mass, Morin et al.(2008). BL Cet, UV Cet - dynamical mass, Kervella et al.(2016). Radius: AD Leo, EQ Peg A/B - radius from spectroscopic effective temperature and bolometric flux, Mann et al.(2015). EV Lac, YZ CMi - theoretical model radius based on photometric mass, Morin et al.(2008). BL Cet, UV Cet - interferometric radius, Kervella et al.(2016). Coronal temperature: Temperature range with peak X-ray emission measure. AD Leo - Güdel et al.(2003); Maggio et al. (2004); Wood et al.(2018). EQ Peg A/B - Liefke et al.(2008). EV Lac - Osten et al.(2006). YZ CMi - Raassen et al.(2007). BL Cet, UV Cet - Audard et al.(2003). Sun - Güdel et al.(1997); Peres et al.(2000). Coronal density: From OVII line ratios. AD Leo, EV Lac, YZ CMi - Ness et al.(2004). EQ Peg A/B - Liefke et al.(2008). Sun - Coronal density models using various types of observations by Allen(1947); Newkirk(1967); Saito et al.(1970); Guhathakurta et al.(1999). OVII line ratios for the quiescent Sun compiled by Ness et al.(2001) are near the low-density limit implying log ne . 9.5.

2 sensitive to ∼3 MK plasma. The targets with measured den- gravity, H = kBT/(µmH g) ≈ (50 Mm)T6R∗/M∗, where R∗ sities all have logne ∼ 10.5. This corresponds to a plasma fre- and M∗ are in solar units, and and µ = 0.6 is the mean molec- quency in the low corona of 1.6 GHz, and second harmonic ular weight of the solar corona. This constant-gravity HSE of 3.2 GHz. However, most solar CMEs do not form shocks model is a simplistic assumption - accounting for the de- low in the corona, accelerating with height as Alfvén speed creased gravity at greater distances from the star would in- declines with height, enabling them to form shocks at heights crease the density at 2R∗ within closed magnetic structures, of ∼ 1.3−2R∗ (Gopalswamy et al. 2009; Prakash et al. 2017). while the decline in the number of closed magnetic structures For now, to estimate plausible start frequencies for stellar and expansion of open magnetic field lines would decrease Type II bursts, we consider the case where a shock forms at the average density with height. r = 2R∗. However, further modeling work is needed in order Using a coronal temperature of 5 MK for active M dwarfs to predict at what range of heights stellar CMEs can exceed and 2 MK for the Sun, we obtain H/R∗ of 0.3-0.5 for our the Alfvén speed and form shocks, which may be particu- target stars and 0.14 for the Sun. Assuming a coronal base larly difficult in the strongly magnetized coronae of active M density logne = 10.5, the plasma frequency at r = 2R∗ should dwarfs. be in the range of ∼300-600 MHz. In contrast, for the Sun, To estimate the density at 2R∗, we assume that density using logne = 8.5, we obtain a plasma frequency of 5 MHz decreases exponentially with height above the base of the at 2R , in agreement to order-of-magnitude with the plasma corona, following the approach of Crosley et al.(2017), who frequency predicted by observational solar coronal density use Sun-as-a-star data to build a framework for interpreta- models (e.g., Guhathakurta et al. 1999). Thus, the maximum tion of stellar Type II bursts. We use the density scale height start frequencies we might expect for CME-associated Type for material in hydrostatic equilibrium (HSE) under constant II bursts on these stars, if the CMEs form shocks at about COHERENT RADIO BURSTSON MDWARFS 7

2R∗, would be ∼0.3-0.6 GHz for first harmonic and 0.6- the parallel-hand correlation products, RR and LL. Polariza- 1.2 GHz for second harmonic emission, within the VLA’s P tion calibration is most important for the cross-hand prod- band (0.2-0.5 GHz) and L band (1-2 GHz), much higher than ucts, so we did not perform any polarization calibration for the start frequencies of most solar Type II bursts. Indeed, in these frequencies (L, S, and C band). contrast to the Sun, active M dwarfs produce abundant co- VLA P band uses linear feeds, for which Stokes V is herent radio bursts at GHz frequencies; AD Leo, EQ Peg, formed from the cross-hand products XY and YX, so polar- and YZ CMi produce 0.2-0.3 bursts per hour at 1.4 GHz ization calibration is required to measure Stokes V in P band. (Abada-Simon & Aubier 1997), although so far it is unknown Full-polarization VLA observations at these frequencies had whether any of those bursts are associated with space weather not been fully commissioned at the time of the observations. events. We were able to perform certain polarization calibration steps By searching for the high-frequency tail of space weather (cross-polarization delay and frequency-dependent leakage) events, this survey takes advantage of the better sensitiv- but not another (cross-polarization phase). The consequence√ ity available at higher frequencies, while complementing of this is that we are able to measure the quantity U 2 +V 2 lower-frequency observations including targeted stellar ob- rather than measuring Stokes U and V independently. As- servations and wide-area transient searches. Targeted stel- suming that our sources have no linear polarization, then this lar observations have been conducted with low-frequency ra- gives the absolute value of Stokes V, allowing us to measure dio facilities including LOFAR (Crosley et al. 2016) and the the degree but not the sense (left or right) of circular polar- MWA (Lynch et al. 2017). Wide-area low-frequency tran- ization. sient searches include projects using the Long Wavelength Array (LWA) (Obenberger et al. 2015), LOFAR (Stewart 3.2. Background Source Subtraction and Dynamic et al. 2016; Prasad et al. 2016), and the Giant Metrewave Ra- Spectroscopy dio Telescope (GMRT) and the MWA (Murphy et al. 2017), After calibration, we shift the phase center to the position including a recent MWA detection of two stars at 200 MHz of the target star. If the star is detected in a Stokes I or V (Lenc et al. 2018). image of an entire observation, then we use the star’s imaged location as the phase center; otherwise we use the star’s ex- 3. DATA ANALYSIS pected position based on positions and proper motions from 3.1. Calibration Hipparcos and/or VLBA (Benz et al. 1998). It is necessary to model and remove background sources The VLA data were calibrated and imaged using the CASA from the visibility data before averaging over all baselines, software package (McMullin et al. 2007). The L band (1- to avoid the contribution of their sidelobes to the stellar flux 2 GHz), S band (2-4 GHz), and C band (4-6 GHz) data were density. Each observation was imaged in Stokes I using calibrated with the CASA VLA calibration pipeline, using CASA’s clean task with multi-frequency synthesis (Rau & the Perley & Butler(2013) flux density scale, followed by an Cornwell 2011) with 2 Taylor terms, which allows the flux additional round of automatic flagging with rflag. The P band density of clean components to vary linearly with frequency. (220-480 MHz) data were also calibrated in CASA, follow- These images of background sources were produced using ing the calibration steps outlined in the CASA Guide “Ba- time and frequency ranges chosen to exclude any bright stel- sic P-band data reduction-CASA4.6” and using the Scaife & lar radio bursts. We created a background model by mask- Heald(2012) flux density scale with L-band model images ing any quiescent stellar emission out of the clean model im- of the flux calibrators. (We bypassed ionospheric TEC cor- age, then used CASA tasks ft and uvsub to subtract the back- rection as it was not supported in CASA 4.6; since it corrects ground model from the visibilities. We developed the code for Faraday rotation of linearly-polarized signals, it does not dynspec1 to average the visibilities over all baselines and to impact our scientific objectives.) We estimate systematic er- extract, analyze, and plot the dynamic spectrum. rors on flux calibration of up to 10% in P band and 3-5% at The end product of the data reduction is dynamic spectra higher frequencies Perley & Butler(2017). (such as in Figure 1a) for all the observations, showing the Stellar coherent radio bursts can have strong circular po- evolution of stellar emission in the time-frequency plane. We larization. Measuring Stokes V provides two benefits: 1) the produce dynamic spectra from interferometric data by aver- sense and degree of circular polarization provide information aging the visibility data over all baselines, generating a sin- on the emission mechanism and the magnetic field orienta- gle complex number per channel per integration. The real tion in the source region; and 2) Stokes V has minimal con- part of this number corresponds to the measured flux density tamination from background sources, offering better sensitiv- ity to strongly polarized bursts than Stokes I. At 1 GHz and above, the VLA correlates circularly polarized signals (RR, 1 The code as used is available at https://github.com/ RL, LR, LL), so Stokes V and Stokes I are both formed from jackievilladsen/dynspec. Consultation is advised before use. 8 VILLADSENETAL. at the phase center at this time and frequency. After suc- to only show pixels with SNR>3, where the noise in each cessful subtraction of bright sources in the field of view, our channel was calculated using the standard deviation (along dynamic spectra should be thermal noise limited. This is in- the time axis) of the imaginary component of the dynamic deed the case for most of our observations. Residual phase spectrum in that channel. The other requirement for identi- errors occasionally led to contamination of dynamic spec- fying a burst is the lack of comparable features in the imag- tra from bright sources, especially for AD Leo and EV Lac. inary component of the baseline-averaged visibilities, which Subsequent self-calibration of observations at >1 GHz, as would indicate contamination by RFI or background sources. needed, allowed us to better model and subtract this back- AppendixA provides an example that illustrates these condi- ground signal. These issues were also prevalent at P band. tions. However, standard self-calibration still resulted in severely For each detected radio burst, we measured a set of ba- dynamic-range-limited images at P band, due to direction sic properties (Table3). Duration and frequency range dependent phase errors that occurred since we observed in are approximate values identified by eye from the dynamic the VLA’s widely-spaced A configuration, resulting in con- spectrum. The presence of burst components with positive siderable sidelobe contamination of the dynamic spectrum or negative frequency drift was also identified by eye in from bright sources across the wide field of view (FWHM the dynamic spectrum; while Section4 discusses general ∼ 2.25◦ in P band). Improving this will require direction de- timescales of frequency drift and Section 5.2.1 examines one pendent self-calibration and source removal (peeling; Noor- event, detailed quantitative studies of duration, bandwidth, dam 2004; Intema et al. 2009), which is not yet available for and frequency drift are left as future work. wideband VLA data through the CASA software package. The peak flux densities quoted in Table3 depend on the We note, therefore, that a future re-analysis of these data with time and frequency resolution of the dynamic spectrum. To direction-dependent self-calibration can achieve more strin- measure peak flux density, rather than impose a single time gent limits in Stokes I at low frequencies. and frequency resolution on all events, long and short, faint and bright, we clipped each observation to just the time range 3.3. Search for Radio Bursts and frequency of the burst, then binned the dynamic spec- trum automatically into roughly 30×30 pixels. For a few We searched for stellar radio bursts by inspecting the faint events, we manually increased the time bins to improve Stokes I and V dynamic spectra by eye. We searched for the SNR. We then took the 98th percentile of the Stokes I flux bursts in both Stokes I and V because Stokes V offered density in the pixels of the dynamic spectrum to represent the greater sensitivity to circularly polarized bursts for fields with peak flux density, choosing this approach to avoid contami- bright background sources, and Stokes I provided sensitivity nation by RFI. The error given for peak flux density is the to unpolarized and weakly polarized bursts. Searches were standard deviation (across all pixels) of the imaginary com- initially carried out in the raw unbinned dynamic spectra, ponent of the baseline-averaged visibilities, which provides with subsequent logarithmic binning in time and frequency an estimate of the noise on an individual pixel in the dynamic to search for events on all timescales probed by our data. spectrum. Errors are largest for low frequency data due to Dynamic spectra of all epochs with detected radio bursts are residuals of background sources. The reported errors do not shown in AppendixB, with each dynamic spectrum binned include systematic errors on flux calibration with the VLA. to a time and frequency resolution chosen to highlight the In addition, the listed peak flux density is an underestimate events in that epoch. While sensitivity depends on resolution, in cases where the flux density varies rapidly on timescales binning to a resolution of 64 MHz and 150 seconds for obser- shorter than ∼3% of the burst duration. vations from 1-6 GHz achieves a typical sensitivity of 1 mJy We also determined the degree of circular polarization of per bin; the thermal sensitivity limit is 0.3-0.6 mJy depending each burst. To do so, we averaged the dynamic spectrum on the band and number of antennas. For 224-482 MHz, bin- over the time and frequency range of each burst to obtain ning to 4 MHz and 300 seconds achieves a typical sensitivity an average Stokes I flux density < SI > and Stokes V flux of 16 mJy in Stokes I and 6 mJy in Stokes V; the thermal density < SV >, then calculated the degree of circular polar- sensitivity limit is 4 mJy. ization rc =< SV > / < SI >. We did not subtract quiescent Each pixel of the dynamic spectrum has a complex value, emission (which is a few mJy or less) before doing so, which the result of averaging complex-valued visibilities over all may result in an underestimate of degree of circular polariza- baselines. A point source at the phase center produces a pos- tion for bursts fainter than ∼20 mJy. The quoted error bars itive signal in the real component of the dynamic spectrum for percent circular polarization were calculated using prop- and no signal in the imaginary component. Bursts were iden- agation of errors for events above 1 GHz, which have small tified visually as a cluster of pixels in the real component fractional errors on degree of circular polarization. For low- of the dynamic spectrum with signal-to-noise ratio (SNR) 2 2 1/2 frequency events, we used (< SU > + < SV > ) instead greater than 3, by making dynamic spectrum plots masked COHERENT RADIO BURSTSON MDWARFS 9 of < SV >, to correct for the lack of cross-hand phase cali- However, the identification of separate bursts within an bration. The low-frequency events had lower SNR than the epoch should be taken as tentative, since the complex high-frequency events, leading to asymmetric error bars, so substructure seen in many events makes it difficult to we calculated a 68% confidence interval or 68%-confidence decide whether to consider two distinct features in the lower limit (noted in the table footnotes), using a Bayesian time-frequency plane as separate events. framework assuming Gaussian errors on Stokes I and V and In spite of the challenges in determining the number of using a flat prior for degree of circular polarization between distinct events and thus the rate of bursts, it is worth do- 0% and 100%. In Table3, a range of values are quoted ing so to inform future observational programs. We es- for certain events, corresponding to burst features at differ- timate the rate of bursts by counting events within one ent frequencies. In these cases the errors are not shown but frequency band at a time, considering events that over- are typically ∼1% for >1 GHz and 10-25% for 0.2-0.5 GHz. lap in time as a single event, thus discounting some Table3 also shows the energy of each event, obtained by of the events in Table3 that are morphologically dis- integrating Stokes I over the time and frequency range listed tinct in the dynamic spectrum but that overlap in time. in the table. Finally, the table lists the SNR with which the In P band (220-480 MHz), we detected 8 events in 42 burst was detected in Stokes I and V. This was calculated hours, a rate of one per 5.3 hours. In L band (1-2 GHz), as the average flux in the time and frequency range of the we detected 15 events in 56 hours, or one per 3.7 hours. burst, divided by the error on that average flux. The error In S band (2-4 GHz), we detected 13 events in 56 on the average flux was determined by first taking the stan- hours, or one per 4.3 hours. And in C band (4-6 GHz), dard deviation across all pixels of the imaginary component we detected 2 events in 14 hours, or one per 7 hours. of the baseline-averaged visibilities, divided by the square As discussed in Section 3.3, these burst rates are for root of the number of dynamic spectrum pixels. For low- a 3σ detection threshold of ∼2-3 mJy in Stokes I and 2 2 1/2 frequency events, we used (< SU > + < SV > ) instead V for 1-6 GHz (for a time and frequency resolution of of < SV > in our SNR calculations, to correct for the lack 64 MHz and 150 seconds), and a 3σ detection thresh- of cross-hand phase calibration. For events on UV Cet that old of ∼50 mJy for Stokes I and ∼20 mJy for Stokes span all observed frequency bands, we list SNR separately V for 220-480 MHz (for a time and frequency resolu- for frequencies below and above 1 GHz to demonstrate that tion of 4 MHz and 300 s). For the most distant star in the events are detected with high significance even in the rel- our survey (EQ Peg at 6.2 pc), a detection threshold of atively noisy low-frequency band. 3 mJy (for the 1-6 GHz events) corresponds to a spec- 14 −1 4. RESULTS tral luminosity of 1.4×10 erg s Hz−1; all but one of the events (the short event on 2013 May 26) fall above The VLA survey detected 22 coherent bursts with diverse this spectral luminosity threshold. properties, summarized below and listed in Table3. We show exemplar dynamic spectra in the text (Figures 1a-1c) to 2. Brightness temperature: We do not have measure- demonstrate the phenomenology of some of the brightest co- ments of source size for these bursts. Coherent sources herent bursts, and we present a full census of the Stokes I and can have millisecond-timescale variation (e.g., Osten V dynamic spectra of all epochs with detected radio bursts & Bastian 2008) indicating small source size and high in AppendixB. For some of the observations of AD Leo and brightness temperatures. Our time resolution of 1 sec- UV Cet, we conducted simultaneous VLBI observing, allow- ond is longer than the light-crossing time for the stel- ing us to trace dynamics both via the dynamic spectra and via lar disks, providing very little constraint on source astrometry with the VLBI data. The VLA data from those size, so we instead calculate the stellar disk-averaged sessions are included in this paper, but the joint analysis of brightness temperature. For the five stars in our sam- the VLA and VLBA data will be presented in subsequent pa- ple, the implied disk-averaged brightness temperature pers. Here we focus on understanding the nature and preva- is ∼ 1011 K for a typical flux density of 20 mJy at 1 lence of coherent radio bursts on active M dwarfs and their GHz. The detected low-frequency events, with flux implications for studies of M dwarf stellar activity and wide- densities of 100-300 mJy, imply the highest brightness field transient surveys. The properties of the population of temperatures or largest source sizes: 0.5-1×1013 K for coherent bursts in the VLA survey are: 200 mJy at 0.35 GHz (assuming a source the size of the stellar disk). However, these may well be signifi- 1. Rate: Coherent bursts were detected in 13 out of 23 cant underestimates of the true brightness temperature epochs on 4 of the 5 stars, with most of these bursts of a much smaller source. detected in multiple bands. As seen in Table3, several epochs had more than one burst, where bursts were dis- 3. Morphology: The morphology of bursts in the time- tinguished by separation in the time-frequency plane. frequency plane provides rich information about the 10 VILLADSENETAL.

70

3.5

3.0 35

2.5 0

2.0 Frequency (GHz) Flux Density (mJy)

-35 1.5

-70 0.0 5.0 10.0 Time (min) since 2015-05-12 00:35:54 UT

Figure 1a. Stokes V dynamic spectrum of a short-duration (minutes-long) burst on YZ CMi, binned to a resolution of 24 MHz and 4 sec. Right circular polarization is red, and left is blue.

40

1.6

20 1.5

1.4

0

1.3 Frequency (GHz) Flux Density (mJy) 1.2 -20

1.1

-40 0.0 60.0 120.0 180.0 Time (min) since 2015-07-05 20:59:21 UT

Figure 1b. Stokes V dynamic spectrum of a long-duration radio burst on AD Leo, binned to a resolution of 4 MHz and 60 sec. Note that the duration and frequency range are dramatically different from the short-duration event in Figure 1a. COHERENT RADIO BURSTSON MDWARFS 11

70

3.5

35

3.0

2.5 0

Frequency (GHz) 2.0 Flux Density (mJy)

-35

1.5

-70 0.0 20.0 40.0 60.0 80.0 Time (min) since 2015-07-04 12:39:02 UT

Figure 1c. Stokes V dynamic spectrum of a long-duration radio burst on UV Cet, binned to a resolution of 12 MHz and 15 sec. phenomena underlying solar radio bursts. We find on the timescale of seconds to minutes expected for that the morphology of stellar radio bursts often de- space weather events, no bursts have both frequency parts from the solar classification scheme but shows a drift on these timescales and emission that continues similarly rich phenomenology. As illustrated by Fig- beyond the lower edge of the observed bands, which ures 1a to 1c, the bursts have diverse morphology in would be a signature of a disturbance continuing to the time/frequency plane, reflecting the diversity in the move outwards from the star. In many cases, the fre- underlying physical processes and conditions respon- quency drift is seen in substructure of a very complex sible for the bursts. A number of bursts show a sharp burst (as in Figure 1c) that does not have an analog cutoff in the frequency spectrum above or below a cer- in solar radio bursts. While the complex substructure tain frequency, as exemplified by the burst on AD Leo could be attributed to a very dynamic and complex in Figure 1b, which drops off rapidly below 1.1 GHz set of source motions, it may also be that the patterns and above 1.6 GHz. Many of the bursts, such as the in the time-frequency plane should not be interpreted UV Cet burst in Figure 1c, show complex substruc- within the solar paradigm (Section 5.1.2). Based on the ture without a clear analog in the classification system lack of features that persist below the minimum fre- of solar radio bursts. We discuss next two aspects of quency observed, as well as the complex structure of morphology that are of particular significance for the many bursts, we have identified no candidate Type II- identification and interpretation of solar radio bursts: like events in this survey. frequency drift and harmonic structure.

4. Frequency drift: Table3 notes whether bursts show 5. Harmonic structure: The majority of metric solar positive or negative frequency drift, or both, or pos- Type II bursts show harmonic structure, with emission sible “unresolved” drift for cases where vertical fea- at similar flux levels at both the fundamental plasma tures in the dynamic spectrum are suggestive of rapid frequency and its second harmonic (Roberts 1959). In frequency drift unresolved by our 1-second integra- spite of the wide frequency coverage of our obser- tion times. These identifications have been determined vations, we detect no bursts with harmonic structure. by visual inspection of the dynamic spectrum at dif- There is only one possible exception, which we con- ferent time and frequency resolutions. While some clude is not likely to be true harmonic structure (Fig- bursts show a downwards frequency drift, including ure 1a; Section 5.2.1). 12 VILLADSENETAL. 180 (L,S), 14 (P) f 1 GHz (P band). < 4 3405 470 300 350 10 150 (L,S),20 6.5 (P) 10 420 (L,S), 17 (P)2 430 (L,S), 14 (P) 400 (L,S), 17 (P) 320 (L,S), 1420 (P) 770 (L,S), 17 70 (P) 770 (L,S), 18 (P) 49 3 1304 280 312 74 52 33 2 12 28 50.3 8.2 361 11 2 55 29 38 34 2 40 0.50.5 350.6 95 137 53 46 53 40 52 0.10.6 30 3.2 13 27 1.5 6.1 7.2 erg) I V ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 22 1 GHz (L, S band) and > 30 m, due to their morphological similarity to long events & ? no 25 ? negative? 2.0 ? no 42 ? no 9.2 e e e e 4 % R negative? 2.2 2 % R negative2 % R 140 negative? 58 1 % L0.2 % L positive positive 411 1413 0.3 % R1 % positive3 % R R 1386 positive negative 148 94 1 % L negative 44.4 3 %2 % L L negative2 % no 12.5 R positive 136 54 2 % L no 30.6 ± ± ± ± ± ± ± ± ± ± ± ± ± 96 % 87 % > > Detected Stellar Radio Bursts. 1 43 - 68 % R1 50 - both 59 % R 5610 both 7950 1 53 - 58 % R both 2470 6 45 2 67 - 70% R positive 1810 22 84 66.5 80 1 77.2 47 65 78 330 62 [82,95] % 2 59 1 53 60 [70,94] % 22 33% L - 90% R 84 unresolved? 75.6 22 75 65 1 52 15 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 3. 83 41 107 111 d d d c 1-6 52 (GHz) Density (mJy) (10 0.3-3.7 79 1.1-1.55 26 a b b long >3.5 h 0.28-0.4 38 long >35 m 0.35-0.385 270 shortshort 25 m 10 m 1-3.7 0.28-0.37 120 20 shortshort 30 s 6 m 1.6-2.2 2.8-4short 31 10 m 9 1-6 9 short 5 m 0.29-0.36 210 short 10 m 1-3.7 42 and their continuation beyond the end of the observations. Only 1-2 GHz data were available for8.2-8.5 this GHz observation. from simultaneous VLBA observations. 68% confidence interval or 68% confidence lowerFor limit UV on Cet’s degree bursts of that circular span polarization all given observed for frequency cases bands, with we asymmetric quote errors. SNR separately for A > symbol on duration indicates thatWe the classify burst these started three before events on or UV ended Cet after with the the observations. long-duration events, which are f c d e a b 2015 Jul 4 long 1.5 h 0.3-8.5 2013 Jun 2 long 1 h 1-4 31 2015 Sep 6 long 1.5 h 0.25-8.5 2015 Sep 5 long >1.5 h 1-2.5 9 2015 Jul 18 long >30 m 0.35-8.5 2015 Jul 19 long >3.5 h 1-1.6 64 2015 May 16 long >20 m 2015 May 13 long >45 m 2-2.7 13 2015 May 15 short 8 m 1.2-2 Star Date Duration Freq Range Peak Flux Polarization Frequency drift? Energy SNR EQ Peg 2015 May 16 long >30 m 1-3 14 UV Cet 2013 May 26 long >25 m AD Leo 2015 Jul 5 long >3.5 h YZ CMi 2015 May 11 long >1.5 h 3-3.7 15 COHERENT RADIO BURSTSON MDWARFS 13

6. Duration: Burst durations range from seconds to bright background sources (AD Leo and EV Lac), and longer than a 4-hour observation. We choose to di- is significant for 220-480 MHz for all targets. 220-480 vide the bursts into two categories: long-duration MHz is also the frequency range (out of the bands ob- (&30 min) and short-duration (seconds to minutes). served) in which we most expect the stars to produce This is a departure from the terminology used to de- CME-associated Type II-like bursts. In contrast to the scribe solar radio bursts, where “long-duration” is used detected stellar bursts, solar Type II bursts generally to describe the minutes-long Type II bursts associated have much less than 50% circular polarization (Kome- with CMEs, events which here would fall in the “short- saroff 1958) with occasional exceptions (Zlobec et al. duration” category. The motivation for adopting this 1993; Thejappa et al. 2003). categorization scheme is: high-speed electron beams Table3 lists the degree of polarization for all the bursts, (responsible for most plasma emission) in the solar and the sense of polarization for all bursts above 1 GHz corona decay on a timescale of milliseconds to sec- (sense of polarization could not be determined below onds due to collisional damping and other mechanisms 1 GHz; Section 3.1). Most of the targets produced (Güdel & Benz 1990), so bursts longer than seconds bursts of both polarizations, although UV Cet shows imply ongoing electron acceleration throughout the a clear preference for right-hand polarization. How- duration of the burst (at our observed frequencies; ever, if we consider only the long-duration bursts, a Type III bursts from high-speed electron beams can pattern starts to emerge. For the three stars with more persist longer as they propagate to very low frequen- than one burst, the long-duration bursts tend to have a cies). Events of seconds to minutes correspond to a consistent sense of circular polarization: left-hand for typical duration for the impulsive phase of a flare or AD Leo and YZ CMi, and right-hand for UV Cet. This for a coronal mass ejection to move a distance com- tentative trend, of consistent sense of polarization in parable to the stellar radius. Thus, our short-duration the long-duration bursts from a given star, is explored category includes the range of durations we expect further in Section 5.3.3 in the context of magnetic field for radio bursts associated with space weather events. measurements of these stars. In contrast, the few short- In contrast, the long-duration bursts require a process duration bursts, such as that in Figure 1a, appear to that produces ongoing electron acceleration over a show arbitrary polarization. timescale of hours. Such long-duration acceleration processes are responsible for some low-frequency ra- 5. INTERPRETATION dio emission from the Sun (solar noise storms) and for In the previous section, we classified our events as short- auroral processes on planets. or long-duration, motivated by the expectation that flares and CMEs should produce bursts that are seconds to minutes We categorize all of our events according to this long, whereas a different electron acceleration process is re- scheme in Table3. The YZ CMi event in Figure 1a quired to produce hours-long bursts. For the purposes of in- falls in the short-duration category, while the AD Leo terpretation, we first highlight some physical principles that and UV Cet bursts in Figures 1b and 1c are classified apply to all events, then consider the short- and long-duration as long-duration. Long-duration bursts are more com- events as separate populations. mon and typically more luminous than short-duration Although the separation of events by duration is physically bursts. In the whole survey, we detect 12-13 long- motivated, we caution that the distinction may be purely ar- duration bursts (depending on whether simultaneous tificial, with all events originating from the same underlying but distinct spectral features on AD Leo on 2015 July process. There may also be multiple phenomena responsible 5 are related) and 8 short-duration bursts. for either the short- or long-duration bursts, as is the case for the complex phenomenology of solar radio bursts. 7. Polarization: Polarization is the one property in which the bursts show a lack of diversity, with all 5.1. Physical Processes Underlying Stellar Radio Bursts bursts having a high degree of circular polarization. Interpretation of the dynamic spectra of stellar coherent ra- Almost all of the bursts fall in the 50-100% range for dio bursts hinges on two interrelated questions: 1) What is degree of circular polarization, with some of the 0.2- the emission mechanism: plasma radiation or electron cy- 0.5 GHz events as low as 40%. It should be noted clotron maser emission? 2) Is frequency drift in the dynamic that for low frequencies, the higher noise due to dy- spectrum due to source motion or to rotational modulation of namic range limits in Stokes I causes a bias towards highly-beamed emission? This section discusses these ques- detecting strongly polarized events. This bias towards tions in light of the observed bursts. strong polarization should not affect 2-6 GHz at all, can have a minor effect for 1-2 GHz for the fields with 5.1.1. Emission Mechanism 14 VILLADSENETAL.

The strong circular polarization observed in most bursts, to the fibrous nature of the solar corona (Chen et al. 2013), combined in many cases with narrowband features in the while GHz-frequency ECM (especially at the second har- frequency spectrum, favors a coherent emission mechanism. monic rather than the fundamental) can escape the corona The two emission mechanisms that may be responsible for if emitted in a low-density cavity (Melrose & Dulk 1982). stellar coherent radio bursts are plasma emission and electron For our data set, the most promising observational indica- cyclotron maser emission (ECM). Identification of the emis- tor of emission mechanism is the degree and sense of circu- sion mechanism is necessary in order to use the emission fre- lar polarization. Plasma emission at the fundamental is ex- quency to determine either plasma density or magnetic field pected to be in the ordinary mode (o-mode) since it is below strength in the source region, which maps to an approximate the minimum frequency at which the x-mode can propagate; source height and potentially a source velocity. The question the second harmonic is most often unpolarized but sometimes of emission mechanism is also a question of which paradigm observed with weak o-mode polarization that is predicted not in which to interpret the coherent bursts of active M dwarfs: to exceed roughly 50% (Melrose et al. 1978). Therefore, the Do active M dwarfs resemble the Sun, whose low-frequency strong polarization observed in almost all events indicates bursts (including the space weather-associated Type II and III that if it is plasma emission, it should be at the fundamen- bursts) are mostly due to plasma emission, with ECM respon- tal frequency and in the o-mode. ECM, in the low-density sible for some high-frequency bursts originating in strongly- limit (ratio of plasma frequency to cyclotron frequency < 0.3; magnetized active regions? Or do active M dwarfs resem- Melrose et al. 1984), should be dominated by emission at the ble auroral emitters, including planets (Zarka 1998), brown fundamental frequency in the extraordinary mode (x-mode), dwarfs (Hallinan et al. 2007), and magnetic massive stars observed to have up to 100% circular polarization. Propa- (Trigilio et al. 2011; Das et al. 2018), which produce periodic gating outwards from a north magnetic pole, o-mode corre- pulses and/or occasional isolated radio bursts due to ECM? sponds to left circular polarization, and x-mode to right cir- There are a number of properties that can help identify cular polarization. Since we observed the long-duration ra- the emission mechanism: brightness temperature (Melrose dio bursts to have a consistent sense of circular polarization 1991), fine structures in the dynamic spectrum (Treumann on a given star, we can compare this sense of polarization 2006; Osten & Bastian 2008), knowledge of plasma den- to stellar magnetic field measurements to assess whether the sity or magnetic field strength in the source (e.g. Morosan emission is in the x-mode or the o-mode and thereby con- et al. 2016), constraints due to absorption (Dulk 1985; Os- strain the emission mechanism for the long-duration events ten & Bastian 2006; Benz et al. 1992), and degree and sense (Section 5.3.3). For the short-duration events, which do not of circular polarization. However, most of these properties have a consistent sense of polarization, we are unable to dif- do not help discriminate between emission mechanisms for ferentiate between fundamental plasma emission or electron our observations, because we do not have the time resolu- cyclotron maser emission. tion needed to detect the ultra-high brightness temperatures or fine structures in the dynamic spectrum associated with 5.1.2. Cause of Frequency Drift ECM, and because measurements of coronal density and Identification of the emission mechanism helps determine magnetic field strength for stars provide only global or large- whether it is appropriate to use frequency drift to measure scale information, allowing a wide range of possible proper- source velocity. Frequency drift cannot always be used to ties for small-scale coronal radio sources. The wide range of measure source velocity because there is more than one po- possible coronal properties means that the observed emission tential cause of frequency drift in coherent bursts: source frequencies (0.28-6 GHz) could be due to either emission motion, rotational modulation, frequency-dependent propa- mechanism: the targets have X-ray measurements of average gation effects, and evolving plasma conditions at a fixed lo- coronal plasma density (∼ 1010.5 cm−3; Table2) and Zeeman cation. Here we consider the two most commonly identified broadening measurements of magnetic field strength (a few causes of frequency drift in solar and planetary radio bursts, kG; Reiners & Basri 2007), corresponding to typical plasma which are source motion and rotational modulation. frequencies of ∼1.6 GHz (but with possible large variation 1. Source motion. Both plasma emission and ECM can around this average) and cyclotron frequencies of 10 GHz . show frequency drift caused by source motion, oc- in the low corona. And while both emission mechanisms curring on timescales of milliseconds to minutes. Of face potentially prohibitive levels of absorption at GHz fre- note are solar Type II and III bursts, which are plasma quencies, due to free-free opacity for plasma emission and emission originating from coronal shock fronts and gyroresonant opacity for ECM, the absorption issues can be electron beams, respectively. Measuring frequency avoided with plausible coronal conditions. GHz-frequency drift rate, combined with a model of the spatial vari- plasma emission may escape the corona when emitted along ation of plasma density or magnetic field strength with a steep density gradient (Benz et al. 1992), which occurs due height h, enables estimation of an apparent source ve- COHERENT RADIO BURSTSON MDWARFS 15

locity (more detailed treatments can be found in, e.g., that long-duration plasma emission may also show fre- Crosley et al. 2017). If a source is moving outwards ra- quency drift due to rotational modulation. dially at constant speed V = dh/dt, the frequency drift In order to detect bulk plasma motion in stellar coronae, it rate ν˙ is: dν dh dν is important to distinguish between true source motion and ν˙ = = V . (1) dh dt dh frequency drift due to rotational modulation or propagation effects. A smoking gun that rules out true source motion is We define a scale height for emission frequency, Hν = repetition of the emission feature once per stellar rotation pe- ν/(dν/dh), which depends on the emission mecha- riod, such as seen on brown dwarfs (Hallinan et al. 2007) and nism and the coronal structure. For plasma emission, CU Virginis (Trigilio et al. 2011). Since our 2- and 4-hour Hν is twice the density scale height, and for cyclotron blocks are shorter than the stars’ rotation periods (Table2), emission, Hν is the magnetic scale length B/(dB/dr). we cannot test periodicity of radio bursts on the stars in this We can then write an expression for velocity: sample, but can rely on other clues. Notably, the UV Cet ν˙  burst in Figure 1c resembles bursts on UV Cet in other epochs V = H (2) ν ν with very similar complex structure in the time-frequency plane. This repetition suggests that the patterns of frequency We apply this equation to an event on YZ CMi in Sec- drift in these event are due to rotational modulation, since it tion 5.2.1. would be unlikely for such a complex set of source motions The timescale for a radio burst caused by a moving to recur in the same pattern in multiple epochs. source is approximately H /V. The longest duration ν 5.2. Short-Duration Events for a burst (or burst substructure) that is caused by To identify stellar space weather events, we look for ra- a moving source will be for the largest expected Hν and smallest expected velocity. Generously taking dio bursts with frequency drift caused by outwards source motion, analogous to solar Type II and III bursts. The Hν ∼ R∗ (larger than the expected hydrostatic equi- librium scale height; see Table2) for our largest star eight short-duration events detected in this survey occur AD Leo, and using a velocity of 1000 km s−1 that is on timescales of seconds to minutes, consistent with the comparable to that of a shock-forming solar CME, we timescales for electron acceleration expected for space see that the timescale should be of order 5 minutes or weather events such as flares and CMEs. However, the ob- less. Thus, while our short-duration events may plau- served stellar short-duration bursts have a number of proper- sibly originate from moving sources, the long-duration ties that diverge from those of solar radio bursts associated events either require some other explanation, or they with geoeffective space weather events. In this section, we must be the combined signal from many different mov- first use the YZ CMi event from Figure 1a to highlight simi- ing sources. larities to and differences from the population of solar radio bursts, then we discuss the properties and physical origins of 2. Rotational modulation. Coherent emission can be the ensemble of short-duration stellar bursts. highly beamed, particularly ECM, which is beamed into the thin surface of a wide cone. (Propagation ef- 5.2.1. Short-Duration Radio Burst on YZ CMi fects in the stellar atmosphere can modify the opening A luminous burst on YZ CMi, shown in Figure 1a, demon- angle of the cone.) As the surface of the cone emit- strates an intriguing resemblance to solar radio bursts as- ted from a particular region passes through our line sociated with source motion, and yet also shows properties of sight, we briefly detect emission from that region. dramatically different from most solar radio bursts. The 10- Frequency drift over time can be produced as a purely minute burst, which spans 1-4 GHz, has a number of dis- geometric effect, as the beamed emission from differ- tinct features in the time-frequency plane, with a range of fre- ent source regions rotates into the line of sight. This quency drift rates from fast to slow. This bears a morpholog- effect has been modeled for Jupiter’s decametric emis- ical resemblance to some solar radio bursts, where features sion, using beam widths of order 1◦ as observed by with a range of negative drift rates (such as Type II and III Kaiser et al.(2000), to explain arc shapes in the dy- bursts) may appear together due to sources moving outwards namic spectrum with frequency structure varying over at different speeds that are associated with one flare/eruptive minutes to hours (Hess et al. 2008), a timescale com- event. However, in contrast to solar Type II and Type III radio parable to our long-duration bursts. Plasma emission bursts, this event shows a high degree of circular polarization can also have narrow angular beaming, as measured whose sense (left or right) varies with frequency and time. for solar Type III bursts at the fundamental plasma fre- Frequency drift rate. This event consists of features with quency (Thejappa et al. 2012), raising the possibility a range of frequency drift rates. One such feature, providing 16 VILLADSENETAL. potential evidence of rapid frequency drift, is a collection of the Alfvén speed in the strongly magnetized coronae of ac- right-polarized vertical spikes in the dynamic spectrum (t∼2- tive M dwarfs is likely of order a few thousand km s−1, so that 4 min in Figure 1a). For these features, no frequency drift is a disturbance moving at a few hundred km s−1 could not form resolved with our 1-second integration time, but they bear a a shock front. Therefore, we prefer an alternative explanation morphological similarity to solar radio bursts caused by high- for the slow frequency drift, such as evolving conditions in a speed electron beams. By analogy, the bandwidth of the ver- source region or modulation by angular beaming. tical spikes may be due to unresolved rapid frequency drift While this burst shows possible evidence of coronal source caused by high source speeds. For example, one such feature motion, including unresolved vertical spikes that may be due in the dynamic spectrum, at t=5.0 minutes, extends from at to rapidly moving sources, it is significant that these fea- least 2.4 GHz to 3.5 GHz, or ∆ν=1.1 GHz. The range of tures do not continue down to low frequencies. The burst frequencies covered within one integration time tint is deter- is not detected in the P band dynamic spectrum nor in a mined by the frequency drift rate ν˙ , the spike duration ∆t cleaned image of the P band data (entire bandwidth) at the (which is ≤ tint), and the emission’s instantaneous fractional times of the higher frequency burst peak, 2015 May 12 0:38- bandwidth fBW: ∆ν = |ν˙ |∆t + fBWν. This implies a lower 0:40 UT. The non-detection in this image puts a 3σ upper limit on frequency drift rate of: limit of 10.8 mJy in Stokes I and 5.4 mJy in Stokes V on the P-band flux density of the burst, lower than the detected ∆ν − fBWν |ν˙ | > . (3) 1-2 GHz flux density of 29.4 mJy (I) and 8.2 mJy (V) and tint 2-4 GHz flux density of 23.1 mJy (I) and 7.6 mJy (V), inte- Observations of fast-drift bursts on AD Leo with milli- grated over the same time range. (For reference, 1 mJy on second time resolution (Osten & Bastian 2006, 2008) mea- this star is 4.3×1013 erg s−1 Hz−1.) In contrast, solar Type III sured a median instantaneous bandwidth of 5% (range from bursts often continue down to very low (kHz) frequencies, <0.5-15% Osten & Bastian 2006, 2008). While we can- which is interpreted as evidence of electrons escaping the not rule out the possibility that the instantaneous bandwidth corona along open field lines (likely accompanied by accel- in this case is larger, if we assume f ∼0.15, we obtain BW erated protons that can impact planetary atmospheres). The |ν˙ | > 0.66 GHz s−1 or |ν/ν˙ | > 0.22 s−1. non-detection of this event at low frequencies means that in Converting frequency drift rate to speed depends on how this case, there is no evidence that accelerated particles are rapidly emission frequency varies with height in the source escaping the corona. region, encapsulated by scale length H in Equation2. H ν ν Polarization structure. Figure2 shows the frequency de- is challenging to estimate without spatially resolved plasma pendence of sense of polarization during the burst peak from density (for plasma emission) or magnetic field measure- 0:38-0:40 UT. During this time, the mapping between fre- ments (for ECM). We consider a range of scale heights from quency and sense of polarization is, roughly: RCP for 1- 0.1R to 1R , which brackets the hydrostatic equilibrium ∗ ∗ 1.5 GHz, LCP for 1.5-1.9 GHz, and RCP above 1.9 GHz, density scale height of 0.34R (Table 3), so this is a plausible ∗ declining to near zero polarization above 3.2 GHz. The pres- range of scale heights for plasma emission. This also covers ence of right polarized burst features simultaneously at fre- a range of possible length scales for decline in magnetic field quencies ν (1-1.5 GHz) and 2ν (∼2-3 GHz) is reminiscent near small-scale features (H ∼ 0.1R ) or in a region dom- ν ∗ of harmonic structure. However, time series of the emis- inated by the global dipole field (H ∼ R ), which contains ν ∗ sion during the burst peak (Figure3) do not show correlated a significant fraction of the total magnetic flux (Morin et al. behavior at ν and 2ν. In addition, it it challenging to ex- 2008). For H ∼ 0.1−1R , Equation2 yields speeds of 1.5% ν ∗ plain this burst’s strong polarization at both ν and 2ν in the to 15% of the speed of light. same sense of polarization using harmonic structure, for ei- Different types of solar radio bursts often appear together, ther plasma emission (which should have a weakly polarized such as the fast-drift Type III and the slow-drift Type II second harmonic; Melrose et al. 1978) or ECM (for which bursts. Similarly, this event’s vertical features, which may the fundamental and harmonic should have opposite polar- be due to unresolved fast frequency drift, are followed within ization if they appear together; e.g., Winglee 1985; Mellott a few minutes by other burst features, some amorphous and et al. 1986). some with gradual negative frequency drift. However, none Instead of harmonic structure, there are a few other pos- of the features bear a clear morphological resemblance to a sible explanations for the multiple alternations in sense of Type II burst, and the frequency drift is too gradual to be polarization as a function of frequency. The reversals in po- caused by a coronal shock front. For instance, a left po- larization may be attributed to: spatial variations in the ratio larized feature at t∼10 minutes in Figure 1a moves from of plasma frequency to cyclotron frequency (Melrose et al. 3.0 to 2.6 GHz in the course of roughly 30 seconds, so 1984; Winglee 1985) or in the energy distribution of the ex- ν/ν˙ ∼ −4.7×10−3 sec−1. Using H ∼ 0.1−1R , we estimate ν ∗ citing electrons (Melrose et al. 1984; Zhao et al. 2016); dif- an apparent outward speed of 100-1000 km s−1. However, COHERENT RADIO BURSTSON MDWARFS 17

0.14 80 1-1.4 GHz 70 RCP 0.12 2-2.8 GHz 60 LCP 0.10 50 0.08 40 0.06 30 0.04 20 0.02 10 0.00

0 RCP Flux Density (mJy) 0.02 10 0 5 10 15 20 25 30 Time-avg Flux Density (mJy) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.06 1.0 0.05 1.5-2 GHz 3-4 GHz 0.04 0.5 0.03

0.0 0.02

0.01 0.5 0.00 LCP Flux Density (mJy)

Degree of Circular Pol. 1.0 0.01 0 5 10 15 20 25 30 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (min) since 2015-05-12 00:25:54.5 Frequency (GHz)

Figure 3. Time series of flux density of the YZ CMi burst from Figure 2. Burst peak spectrum for the YZ CMi event from Fig- Figure 1a. The right polarized burst features (top) and left polarized ure 1a, spanning 2015 May 12 0:38-0:40 UT. (top) Right circular burst features (bottom) are integrated over frequency ranges corre- polarization (RCP) and left circular polarization (LCP) flux density sponding to distinct spectral features. While all frequencies show spectra, where polarized flux density is defined using the conven- flare activity at the same time, the features at ν (black line) and 2ν tion that I=(RCP+LCP)/2. The 1-σ statistical error in each channel (red line) with shared polarization do not have similar time variation is shown as an envelope around each spectrum. (bottom) 68% con- within the burst. fidence interval for degree of circular polarization versus frequency; +1 is 100% right polarized and -1 is 100% left polarized. The short-duration bursts all have strong circular polariza- tion (50-100%); this is true for most short-duration bursts in ferent emission mechanisms (plasma and ECM) contributing the literature as well, with only a few cases of unpolarized x-mode and o-mode; or multiple interconnected source re- or weakly polarized bursts (Kellett et al. 2002). The short- gions with opposite magnetic polarity. None of the scenarios duration bursts in this survey do not show evidence of har- provide a straightforward explanation for why there is more monic structure, with the possible exception of some features than one polarization reversal with increasing frequency, and in the YZ CMi event. Significantly, while multiple events we find no definitive way of differentiating between them show frequency drift, the frequency drift is either too slow with the available data. However, the last scenario, two sepa- to be associated with a coronal shock, or too fast to be re- rate but connected source regions, would permit independent solved (if it is indeed frequency drift) and therefore much time variation in the two polarizations (due to a disturbance too fast for a coronal shock. In addition, no short-duration affecting both regions, but causing different electron acceler- events continue to drift to frequencies below the edge of our ation time profiles in the two source regions), which would observing band. also help explain why the right and left polarized features do The lack of harmonic structure and strong degree of po- not line up perfectly in time, and certain features show up in larization of the stellar short-duration coherent bursts are only one polarization, such as the vertical spikes seen in RCP both characteristic of the electron cyclotron maser, but may at 2.4 to 3.5 GHz. also be explained by fundamental plasma emission. In- deed, these properties are characteristic of solar Type I noise 5.2.2. Physical Origins of Short-Duration Events storms (Komesaroff 1958; Jaeggi & Benz 1982), which are The YZ CMi event demonstrates attributes characteristic attributed to fundamental plasma emission (Melrose 1980), of the population of short-duration stellar coherent bursts. but which tend to be long-duration events. In contrast, the 18 VILLADSENETAL. short-duration plasma-emission solar Type II bursts (which of radio bursts in the extreme coronae of active M dwarfs trace CMEs) and Type III bursts (which trace fast electron than on the Sun. If so, we expect that the radio bursts beams) most often show weak to moderate circular polar- should be associated with flares at optical/X-ray/UV wave- ization that only occasionally exceeds ∼50% (Zlobec et al. lengths. Past multi-wavelength studies have found that radio 1993; Dulk & Suzuki 1980), and the fundamental and second bursts on active M dwarfs are only sometimes associated with harmonic are often detected together (Roberts 1959; Smerd flares at other wavelengths (Kahler et al. 1982; Nelson et al. 1976), although fundamental emission may be suppressed 1986; Kundu et al. 1988; Güdel et al. 1996; van den Oord above ∼100 MHz (Dulk & Suzuki 1980). Short-duration et al. 1996; Gagné et al. 1998; Osten et al. 2005), but these solar bursts can show a high degree of circular polarization studies used radio time series. With the additional infor- (millisecond spike bursts; Benz et al. 1982; Nonino et al. mation from wide-bandwidth dynamic spectroscopy, multi- 1986; Staehli & Magun 1986), but such bursts are generally wavelength campaigns can help sort short-duration coherent attributed to ECM (Melrose 1994). radio bursts into different populations based on flare associ- The sense of circular polarization of the short-duration ation, identifying which radio bursts may be associated with events provides an additional clue to their origins: multiple space weather events. events on the same star may show different polarizations, or a single event may have both right and left polarized fea- 5.2.3. Non-Detection of Radio-Loud CMEs tures (Figure 1a). This arbitrary polarization implies that the Further work is needed to characterize the population of bursts originate in regions with apparently random magnetic stellar short-duration coherent bursts and determine their polarity, as expected for the small-scale magnetic features physical origins. However, none of the short-duration bursts that should dominate most of the stellar surface (since only detected by the survey are a clear analog to solar Type II ∼14% of magnetic flux is in the large-scale field for active bursts produced by coronal shock fronts (which are often mid-M dwarfs; Reiners & Basri 2009). This is consistent driven by super-Alfvénic CMEs). For this reason, we calcu- with the expectation for coronal disturbances (such as flares) late our flux density detection threshold for radio-loud coro- driven by reconnection processes associated with the evolu- nal shock fronts around these stars, and scale it to a distance tion of small-scale magnetic structures. of 1 AU to contrast it to the flux densities observed for solar In contrast to many solar Type II and Type III bursts, which Type II bursts. We also consider whether our non-detection can continue down to kHz frequencies, none of the short- may be due to the rate of shock-forming CMEs expected on duration events appear to continue to frequencies below the these stars based on their energetic flare rates. edge of our observing band. As discussed above for the We concentrate here on the 220-480 MHz band, since, as YZ CMi event, this means that whatever coronal disturbances discussed in Section 2.2, it is more likely for stellar Type II- are responsible for the short-duration bursts, they likely do like bursts to occur in this band than at higher frequencies. not propagate freely away from the star into interplanetary To put an upper limit on the possible flux density of Type II- space. However, another possibility is that disturbances fur- like bursts during our observations, it is helpful to predict ther from the star do not fulfill the conditions for coherent the bandwidth and duration of such events. The bandwidth emission or they produce directional coherent emission that is determined by the range of plasma densities in the emit- is consistently beamed away from us. It is possible that ting region, difficult to predict a priori, so we assume a typ- such events are still caused by the same phenomena as solar ical solar value for instantaneous fractional bandwidth of bursts. For example, short-duration bursts could be caused by ∆ν/ν ∼ 0.2 − 0.4 (Mann et al. 1995), where 0.2 corresponds a shock front that only forms briefly when a coronal distur- to a burst bandwidth of 70 MHz at an observing frequency bance (such as a CME) passes through a weakly magnetized of 350 MHz. The duration is then the time for a burst with region where it exceeds the Alfvén speed. However, it is also drift rate ν˙ to cross the burst bandwidth: ∆t = ∆ν/ν˙ . Using possible that the bandwidth and duration of these short events a CME speed of 2000 km s−1 (see discussion of Alfvén speed are determined by an angular beaming pattern, rather than by later in this section) and a density scale height of 75 Mm source motion. (middle of the range in Table2), we use Equation2 to ob- The population of short-duration coherent bursts do not tain ν/ν˙ = V/(2H) ∼ 1/(70 s) and ∆t ∼15 sec. In a dynamic have clear analogs within the solar classification system, spectrum pixel of 70 MHz and 15 sec, for the 220-480 MHz in terms of polarization, harmonic structure, and frequency band, we obtain a typical Stokes I sensitivity of 17 mJy. We range and drift rate, preventing an immediate interpreta- consider only the Stokes I sensitivity, and not Stokes V, since tion of these bursts in terms of space weather. However, solar Type II bursts tend to have fairly weak polarization. Our it is still possible that these short-duration bursts are asso- 3σ upper limit on Stokes I flux density of possible Type II ciated with coronal disturbances that drive space weather, bursts during our 42 hours of 220-480 MHz observations is but that such coronal disturbances result in different types roughly 50 mJy. COHERENT RADIO BURSTSON MDWARFS 19

We scale our survey’s detection threshold to 1 AU to com- CME association rate alone cannot be used to predict pare to the flux densities of observed solar Type II bursts to the rate of radio-loud CMEs at 220 MHz and above for evaluate whether sensitivity may cause the lack of Type II our sensitivity threshold. detections. If these stars were at 1 AU, the 50 mJy upper limit on flux density would correspond to an upper limit of 2. Rate of flares expected to be associated with fast CMEs 1.6-8.2×106 solar flux units (SFU), where 106 SFU at 1 AU that can form shocks. In the solar corona, more en- corresponds to a spectral luminosity of 2.8×1014 erg/s/Hz. ergetic flares tend to be associated with faster CMEs There is limited information available on solar flux densi- (Yashiro & Gopalswamy 2009) that are more likely ties at metric wavelengths. The first observed solar Type II to form shocks and produce radio bursts. To form burst (Payne-Scott et al. 1947) peaked at 107 SFU at 60 MHz. a shock, a CME must exceed the local fast magne- Nelson & Melrose(1985) report that the brightest metric tosonic speed, which is roughly the Alfvén speed in bursts observed by the Culgoora radioheliograph are of order the magnetically-dominated corona. The Alfvén speed 105 SFU, and flux densities can be as low as 1 SFU. Thus, the is sensitivity of our survey would be enough to detect the stellar   −1/2 −1
B  ne  equivalent of only the most exceptionally bright solar Type II vA = 1940 km s . (4) 50 G 109.5 cm−3 bursts, so it is plausible that radio-loud CMEs on these stars may be occurring below the detection limit. Crosley & Os- To assess what CME speed is required to form a shock, ten(2018b) assess detectability of stellar Type II bursts for we estimate the Alfvén speed at 2R∗ for our targets. their observations of EQ Peg with all 27 VLA antennas, find- To do so, we use the density at 2R∗ that corresponds ing that a CME shock with the maximum observed bright- to the plasma frequency estimated in Table2. The 14 ness temperatures for solar Type II bursts of 10 K(Benz large-scale magnetic field of the target stars is mostly & Thejappa 1988), and source size comparable to the stellar poloidal, with a strong dipole component of order a disk, would be barely observable, but they note that if stellar few hundred Gauss (Morin et al. 2008; Kochukhov & 18 Type II bursts have higher brightness temperatures of 10 K, Lavail 2017). We therefore estimate that a typical field 3 consistent with the high brightness temperatures observed in strength at 2R∗ is of order (400 G)/2 = 50 G. We then −1 some stellar coherent bursts (Osten & Bastian 2008), these obtain Alfvén speeds at 2R∗ of 1600 to 3500 km s events should be easily detectable by the VLA. for our targets, where the later-type stars have lower Given the uncertainty in expected brightness temperature Alfvén speeds. This threshold velocity for CMEs to for stellar Type II bursts, the non-detection may be caused form radio-loud shocks is significantly higher for flare by sensitivity or by the rate of CME shocks around the ob- stars than for the Sun: the solar Alfvén speed is of or- −1 served stars. We can compare our non-detection of radio- der 500 km s at heights above 1.2R (Gopalswamy loud CMEs during this survey to the rate of energetic flares et al. 2001; Mann et al. 2003). at other wavelengths to test our expectations based on so- We next estimate the typical energy of a stellar flare lar flare-CME correlations. We compare to flare rate in two associated with such a fast CME, based on solar cor- ways: relations between CME properties and flare energy. 1. Rate of flares expected to be associated with CMEs. Crosley et al.(2016) combine the correlations between The most energetic solar flares show an almost 100% solar flares and CME properties from Aarnio et al. association rate with CMEs (Yashiro & Gopalswamy (2012) and Osten & Wolk(2015) to derive an equa- 2009). This is true for solar flares with GOES X-ray tion predicting stellar U-band flare energy from CME −2 30 5.4 fluence above 0.2 J m , which corresponds to a U- velocity: EU = (9.8 × 10 erg)v (from their Equa- band stellar flare energy of 6×1030 erg (using the flare tion 7). Our Alfvén speed estimates correspond to energy scaling relationships of Osten & Wolk 2015). U-band flare energies of 1032 to 1034 erg for our tar- Based on the flare frequency distributions of Lacy et al. gets, and the flare frequency distributions of Lacy et al. (1976), a flare above this energy is expected to occur (1976) predict one such energetic flare per: 200 hours every: 7 hours on AD Leo, 1 hour on EQ Peg (con- on EV Lac or YZ CMi, 400 hours on AD Leo and sistent with the prediction of Crosley & Osten 2018a), UV Cet, and 1800 hours on EQ Peg. (In contrast, 4 hours on EV Lac, 3 hours on YZ CMi, 15 hours on Crosley & Osten(2018b) find roughly the same thresh- UV Cet. Based on our survey’s duration on each tar- old U-band flare energy for EQ Peg of 1034 erg, but get, we expect that during the survey about 11 optical predict that such a flare occurs once per 27 hours.) This flares occurred at an energy high enough that such a corresponds to only a 15% chance that during our sur- flare would almost certainly be associated with a CME vey a sufficiently energetic flare occurred to produce a if it occurred on the Sun. Therefore, the solar flare- fast shock-forming (and thus radio-loud) CME, if stel- 20 VILLADSENETAL.

lar flares follow the same flare-CME correlations as so- sion is an ongoing subject of debate (Benz & Güdel 1994; lar flares. Airapetian & Holman 1998; Kellett et al. 2002), and it is This estimation process is extremely uncertain due to unclear whether the incoherent and coherent emission have the order-of-magnitude scatter in scaling relationships, shared or distinct acceleration mechanisms. Solar and plan- the steep dependence of predicted U-band flare energy etary processes both provide examples of possible acceler- on CME speed, and ignorance of conditions in the stel- ation processes responsible for the long-duration coherent lar corona (whose strong magnetic fields may suppress emission. Possible explanations within the paradigm of solar or slow CMEs; Alvarado-Gómez et al. 2018). This cal- and stellar activity include: ongoing magnetic reconnection culation does serve, however, to demonstrate that the caused by emerging magnetic flux (thought to be responsi- lack of detections of stellar Type II-like radio bursts ble for Type I solar storms; e.g., Stewart et al. 1986; Bentley does not necessarily imply a lack of CMEs; it could et al. 2000); quasi-steady acceleration due to frequent small also be caused by the rarity of CMEs fast enough to ex- flares (discussed in the context of active binaries by Lefèvre ceed the high Alfvén speed in the strongly magnetized et al. 1994); gradual energy release during a flare decay phase coronae of active M dwarfs. It remains a possibility too (which may explain long M dwarf flare decay times; Kowal- that stellar Type II-like bursts are occurring in the ob- ski et al. 2013), possibly due to post-eruptive magnetic recon- served frequency range, but that our observations have figuration (Katsova et al. 1999); or reconnection in an equato- not reached the requisite sensitivity. rial current sheet formed by the stellar wind (proposed to ex- plain X-ray and radio emission from magnetic massive stars; Due to the range of factors that may cause a non-detection Havnes & Goertz 1984; Linsky et al. 1992). Possible expla- of stellar Type II bursts, our observations do not constrain the nations within the paradigm of planetary and brown dwarf occurrence rate of stellar coronal mass ejections. However, auroral radio emissions (Zarka 1998; Hallinan et al. 2015) these observations demonstrate that the observed population include: interaction of the large-scale magnetosphere with of coherent radio bursts on active M dwarfs is not caused plasma distant from the star (co-rotation breakdown, analo- by the mechanism of plasma emission from a CME shock gous to Jupiter’s main auroral oval) or currents on a magnetic front, and therefore that the current-generation VLA does not field line connected to a close-in satellite (analogous to the provide a systematic method to detect and characterize stellar Jupiter-Io interaction). The Sun is not known to produce such CMEs on active M dwarfs. auroral emission, but the strong large-scale magnetic field of these stars (0.1-1 kG in the dipole field, in contrast to about 5.3. Long-duration Events - Solar Storms or Ultracool Dwarf Aurorae? 1 G for the Sun) means that they are better able to generate powerful currents through magnetospheric processes distant The long-duration coherent bursts observed in this sur- from the star. vey share the strong circular polarization of short-duration The AD Leo and UV Cet bursts in Figures 1b and 1c pro- events, indicating that they may originate from the same vide evidence that the acceleration mechanism operates over emission process. However, we can derive additional clues a timescale of weeks to months. The AD Leo burst is nar- about the origins of long-duration events from their per- rowband, with sharply defined lower and upper cutoff fre- sistence over hours, their frequency dependence, and their quencies at 1.1 and 1.6 GHz. An observation 2 weeks later consistent sense of polarization. These properties may be detects nearly identical emission (Figure 8e in the appendix) considered within the framework of solar radio bursts or in throughout that entire 4-hour observation as well, suggesting the framework of periodic radio aurorae produced by brown that this event might be ongoing for 2 weeks or more. With dwarfs and planets, or they may belong to a population of its narrow bandwidth, strong circular polarization, and po- radio bursts unique to active M dwarfs. tentially weeks-long duration, this event bears a resemblance 5.3.1. Hours-Long Duration to solar Type I noise storms (Elgarøy 1977). Type I noise storms are attributed to fundamental plasma emission from Stellar coherent emission processes derive energy from a a closed magnetic field structure, where the lowest density positive gradient in the electron velocity distribution (such within the magnetic field structure determines the low fre- as an excess of high-speed electrons). The observed long- quency cutoff of the burst. Type I noise storms can last for duration bursts require ongoing electron acceleration to sup- days, associated with the emergence of new magnetic flux ply these high-speed electrons throughout their hours-long through the photosphere (Stewart et al. 1986). However, the duration. The presence of such an ongoing acceleration pro- strongly polarized emission in Type I storms consists of short cess is perhaps not surprising, given that these stars contin- sub-second spikes of emission, whereas the AD Leo burst uously produce non-thermal incoherent quiescent emission flux density varies smoothly (to within our sensitivity for our at GHz frequencies (Güdel 1994). The electron accelera- 1-second integration time). In addition, the sense of polariza- tion process responsible for the incoherent quiescent emis- COHERENT RADIO BURSTSON MDWARFS 21 tion of the AD Leo bursts is consistent with the x-mode (Sec- magnetic field averaged across the visible hemisphere of the tion 5.3.3), whereas solar Type I storms are polarized in the star) has the same sign at all rotational phases, implying that sense of the o-mode. Nevertheless, the narrow bandwidth of the same magnetic pole is visible throughout the entire rota- the AD Leo burst (and of the long-duration bursts observed tion period. Table4 lists the observed polarity of the large- on YZ CMi; Figure 8c in the appendix) may be caused by scale field of our targets and the sense of polarization of long- emission from within a closed magnetic structure, analogous duration radio bursts from this survey and from the literature. to Type I storms. Alternatively, the narrow bandwidth may be For long-duration bursts above 1 GHz, the radio emission is attributed to an angular beaming pattern for which only cer- LCP for stars with the magnetic south pole visible (AD Leo tain frequencies are observable at Earth. The AD Leo burst and YZ CMi) and RCP for stars with the magnetic north pole has narrowband substructure with gradual positive frequency visible (EQ Peg and UV Cet). This is consistent with emis- drift, which may also be due to modulation by an angular sion in the extraordinary mode (x-mode) relative to the po- beaming pattern. larity of the large-scale field. As discussed in Section 5.1.2, the UV Cet burst in Fig- The observed x-mode polarization and the high degree of ure 1c strongly resembles events detected in other epochs circular polarization of the long-duration coherent bursts are separated by months. Due to the complexity and repeated na- characteristic of electron cyclotron maser emission. A low- ture of this burst, it is most easily explained as periodic radio density environment (νp/νc . 0.3) is required to explain the bursts analogous to those seen on planets and brown dwarfs, the x-mode polarization (Melrose et al. 1984) and the escape where the complex pattern in the time-frequency plane is due of the radiation in spite of gyroresonant opacity (Melrose & to rotational modulation of angularly beamed emission. Dulk 1982; Za˘itsev et al. 2005). For 1 GHz emission, this implies electron densities of 109 cm−3 in the source re- 5.3.2. Frequency Dependence . gion, significantly lower than the average coronal densities Within this survey, luminous long-duration bursts are most of order 1010.5 cm−3 (Section 2.2). However, if any such hot, abundant at 1-1.4 GHz compared to lower and higher fre- diffuse cavities exist in the corona, the emission can escape quencies (Table3; Section 6.1). While the peak frequency to greater heights via multiple reflections along the cavity, may vary somewhat from epoch to epoch or from star to a process seen in Earth’s auroral kilometric radiation (e.g., star, this population of bursts stands in contrast to the Sun, Zarka 1998). The long-duration bursts at 1-6 GHz originate on which luminous bursts are an order of magnitude more in regions with field strengths of 0.36-2.1 kG (if fundamen- frequent below 1 GHz than in bands above 1 GHz (Nita tal emission) or 0.18-1.1 kG (if second harmonic). We ex- et al. 2002). The abundance of >1 GHz coherent radio bursts pect such field strengths to occur in the low corona, relatively compared to the Sun can be attributed to the stronger mag- close to the star, so that we only observe the polarization cor- netic field strengths (and cyclotron frequency) and higher responding to the visible magnetic pole. plasma densities (and plasma frequency) in the coronae of In contrast, low frequencies (<1 GHz) correspond to active M dwarfs. The decline of burst occurrence rate below greater heights in the stellar atmosphere, which are less 1 GHz observed on these stars indicates that the population of likely to be obscured by the star. We therefore expect that bursts observed by this survey are dominated by disturbances low frequency bursts of either polarization may be observed. that are restricted to the low corona, where magnetic field Indeed, bursts observed below 0.5 GHz on UV Cet (Lynch 10 −3 strengths are >300 G and/or plasma densities are >10 cm . et al. 2017) and YZ CMi (Davis et al. 1978) sometimes show The presence of this population of coherent bursts peaking at opposite polarization compared to higher frequencies. 1-1.4 GHz, which has no analog on the Sun, suggests that a The agreement between radio polarization and polarity of non-solar process may be responsible for these bursts. the large-scale magnetic field indicates consistent magnetic 5.3.3. Consistent Sense of Polarization polarity in the source region, suggestive of an electron ac- celeration process that populates the large-scale field. In a On a given star, the long-duration bursts above 1 GHz solar-like corona, flares should not selectively occur in re- show a consistent sense of circular polarization. Our tar- gions that match the polarity of the large-scale field. Instead, gets all have magnetic field measurements from optical/IR the electron acceleration is likely occurring at a distance from spectropolarimetry (Morin et al. 2008; Kochukhov & Lavail the star where the large-scale field dominates, then electrons 2017), providing the opportunity to compare the dominant ra- propagate along field lines down to the low corona where dio polarization to the polarity of the large-scale photospheric they produce radio emission. This is analogous to the auroral magnetic field. current systems on planets and brown dwarfs. However, we The majority of active mid M dwarfs have a strong large- note that one other possible explanation (instead of source scale magnetic field that is nearly rotationally symmetric and regions sharing the polarity of the large-scale field) is weak- poloidal (Morin et al. 2008). For all of our targets except mode coupling, which would cause all x-mode emission to EV Lac, the measured longitudinal field (the line-of-sight 22 VILLADSENETAL.

Table 4. Magnetic Polarity and Long-Duration Radio Burst Polarization.

Star Visible Magnetic Pole Epoch Reference Long-duration Radio Number Epoch Reference Burst Polarization of Events LCP (1.4 GHz) 1 1985 3 AD Leo S 2007, 2008 1 LCP (>1 GHz) 3 2015 * RCP (<1 GHz) 2 2015 * RCP (1.5 GHz) 1 1985 4 EQ Peg A/B N/N a 2006 1 RCP (1-3 GHz) 1 2015 * EV Lac N, S b 2006, 2007 1 no bursts RCP? (0.41 GHz) c 2 1977 5 LCP (4.9 GHz) d 1 1983 6 LCP (1.5 GHz) 1 1984 6 YZ CMi S 2007, 2008 1 LCP (1.5 GHz) 1 1985 4 LCP (1.5 GHz) 1 1987 7 LCP (1.8-4 GHz) 2 2015 * RCP (1.5 GHz) 1 1985 4 BL Cet/UV Cet N/N a 2013 2 RCP (0.2-8.5 GHz) e 6 2013, 2015 * RCP, LCP (0.15 GHz) 4 2015 8

NOTE—Long-duration radio bursts are included from this work and the literature. See also the compilation in Kellett et al.(2002). aBoth binary components have the north magnetic pole visible. bThe sign of the net longitudinal field on EV Lac varies with rotational phase, indicating that both magnetic poles rotate in and out of view over the course of the rotation period. c Observations had only right-polarized feeds, so burst may have had an LCP component. dClassified by the authors as slowly-variable quiescent emission, but included here due to its nearly 100% circular polarization. e Two bursts on UV Cet have a faint LCP signal that appears before the start of the RCP emission. References— (*) This work. (1) Morin et al.(2008). (2) Kochukhov & Lavail(2017). (3) White et al.(1986). (4) Kundu et al.(1988). (5) Davis et al.(1978). (6) Lang & Willson(1986). (7) Lang & Willson(1988). (8) Lynch et al.(2017).

match the handedness (R or L) of the x-mode in the large- over decades (Table4; and Kellett et al. 2002). There is only scale field regardless of the polarity of the source region (e.g., one pulsing ultracool dwarf with a spectropolarimetric mea- Benz 2002). surement of the magnetic field, and the relationship between While the polarization in the x-mode relative to the large- the polarization of radio pulses and magnetic field orienta- scale field is suggestive of auroral processes, the long- tion is ambiguous: M8.5 dwarf LSR J1835+3259 produced duration coherent bursts observed on active M dwarfs in LCP pulses in 2006 (Hallinan et al. 2008) and RCP in 2011 this survey are not a perfect analog to the periodic pulsed (Hallinan et al. 2015), and Berdyugina et al.(2017) in 2012 radio emission from Jupiter and brown dwarfs. Other than detected a longitudinal magnetic field oriented away from for the set of similar bursts on UV Cet, there is no evidence the observer (corresponding to a southern magnetic pole). that most of these long-duration M dwarf bursts are peri- odic. Depending on the geometry (shape of emitting region, 5.3.4. Time Evolution of Magnetic Activity inclination of the rotation axis, magnetic dipole axis, beam In the Sun, various magnetic activity properties, including opening angle, and propagation effects), auroral radio emis- the rate of flares and coronal mass ejections, are linked to the sion from planets and brown dwarfs can have features of both evolution of the Sun’s global magnetic field throughout the polarizations, and the duration of individual pulses may be solar cycle, as well as to small-scale evolution of the mag- quite short or long. Ultracool dwarf radio pulses sometimes netic field as active regions emerge and decay. The Sun’s vary in sense of polarization between epochs, perhaps in- large-scale magnetic field reverses polarity every 11 years. dicative of magnetic reversals (Route 2016), whereas active It is unknown whether such magnetic polarity reversals will M dwarfs seem to consistently prefer one radio polarization also occur on active mid-M dwarfs, whose magnetic dynamo COHERENT RADIO BURSTSON MDWARFS 23 operates under different conditions than on the Sun (rapid ro- & Willson 1986, 1988; White et al. 1986; Kundu et al. 1988; tation and fully convective interiors, similar to the ultracool Slee et al. 2003), these observations have all used interferom- dwarf observations in Route 2016). eters. Some long-duration coherent bursts may also be clas- In contrast to changes in brown dwarf radio burst polar- sified by other authors as slowly-variable quiescent emission ization that Route(2016) interpret as potential evidence of (e.g., Figure 1 in Kundu et al. 1988). This survey’s broad magnetic polarity reversals, the consistent sense of polariza- bandwidth may also have helped improve the detection rate tion of radio bursts in our survey, in agreement with non- of narrowband coherent emission. contemporaneous magnetic measurements, suggests a lack of 6. IMPLICATIONS FOR TRANSIENT SURVEYS magnetic reversals between the spectropolarimetric observa- tions in 2007-2012 and the radio observations in 2013-2015. Stellar flares from active M dwarfs and close binaries are Kellett et al.(2002) compiled observations of UV Cet and expected to be among the most common types of radio tran- YZ CMi from 1983-1996, finding that the preponderance sients at decimetric wavelengths (Osten 2008; Williams et al. of radio bursts have polarizations that agree with the long- 2013; Mooley et al. 2016). This expectation applies to ongo- duration events in our survey, indicating that these stars may ing and upcoming transient surveys by telescopes including not have undergone a polarity reversal in over 30 years. The ASKAP, MeerKAT, and the VLA. Long-duration coherent lack of magnetic reversals is consistent with the findings of bursts should dominate the population of flare star transients Vida et al.(2016), who perform Doppler imaging of active at low frequencies (below a few GHz). However, due to the mid-M dwarf V374 Peg, revealing a stable spot pattern on narrowband nature of coherent emission, estimation of the the star over 15 years. This survey adds to the evidence that transient rate is complicated because the frequency coverage active M dwarfs may go decades without polarity reversals, of a given transient survey is not an exact match to that of but with so few objects studied so far (in this survey and in past stellar observations. The wideband nature of our obser- the literature), this pattern cannot be generalized to all active vations makes it possible to estimate the active M dwarf tran- M dwarfs. sient rate adjusted for the frequency coverage of individual While the large-scale magnetic field of these stars appears surveys. to be stable, the majority of magnetic flux is still in small- To characterize the dependence of transient density on fre- scale magnetic features (Reiners & Basri 2009) that evolve quency, we first divide our data into√ sub-bands with equal on timescales of weeks to years (Giles et al. 2017). This fractional bandwidth, νmax/νmin = 2, and calculate transient may drive time variation in the observed levels of magnetic density for each sub-band (Section 6.1). We then apply the activity, including the rate of coherent bursts. Within our sur- same process to the frequency bands of three ongoing or up- vey, we note a higher burst detection rate on AD Leo in 2015 coming transient surveys (Section 6.2): the ASKAP VAST (3 out of 5 epochs) compared to 2013 (0 out of 4 epochs). survey, the MeerKAT ThunderKAT survey, and the VLA Sky This difference is largely due to long-duration bursts (with Survey (VLASS). two nearly identical long-duration bursts detected two weeks 6.1. Transient Density Dependence on Frequency apart in 2015), consistent with an acceleration mechanism for long-duration bursts that evolves on timescales of weeks To calculate transient density, we take three steps: 1) For to years. a given frequency band, calculate the burst duty cycle (frac- Some past observations at ∼1.5 GHz have found relatively tion of time spent bursting) as a function of luminosity. 2) low rates of coherent bursts compared to our survey. While Estimate the volume density of active M dwarfs. 3) For a we detected 1 burst per 3.7 hours at 1-2 GHz, Osten & Bas- given frequency band, calculate the expected transient den- tian(2006) report 1 per 8 hours on AD Leo at 1.1-1.6 GHz sity, which is the number of bursts (above a given flux den- with Arecibo (16 hours total), and Abada-Simon & Aubier sity) per area on the sky at an instant in time. (1997) report 1 per 7 hours on AD Leo, EQ Peg, and YZ CMi 6.1.1. Coherent Burst Duty Cycle at 1.4 GHz with Arecibo (49.4 hours total, counting distinct We divide our data into five sub-bands with equal frac- events by requiring >5 minutes separation). This difference tional bandwidth: 340-480 MHz, 1-1.4 GHz, 1.4-2 GHz, 2- can be largely attributed to their lack of detection of long- 2.8 GHz, and 2.8-4 GHz. We use constant fractional band- duration bursts; our rate of detection of short-duration bursts width ν /ν so that, for a simple exponential coronal at 1-2 GHz is only 1 per 11.2 hours (5 in 56 hours). The max min model (as in Section 2.2 and Equation2), each sub-band will lack of detection of long-duration bursts in these surveys may correspond to roughly the same interval in physical height be due to the use of a single dish telescope, which requires ∆h = h(ν ) − h(ν ) = H lnν /ν
. We will identify subtraction of smooth time variations to remove gain varia- min max ν max min bursts as times when the Stokes I luminosity time series for tions and noise. While there have been other reports of long- a sub-band is above a certain threshold, using the same lu- duration bursts on active M dwarfs (Davis et al. 1978; Lang minosity threshold for all sub-bands. We originally covered 24 VILLADSENETAL.

340-480 MHz 1-1.4 GHz 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

0.2 0.2

0.4 0.4

0.6 0.6 0 30000 60000 90000 120000 0 30000 60000 90000 120000

1.4-2 GHz 2-2.8 GHz 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

0.2 0.2

Flux Density (Jy) at 1 pc 0.4 0.4

0.6 0.6 0 30000 60000 90000 120000 0 30000 60000 90000 120000 Time in seconds (all obs concatenated) 2.8-4 GHz 1.0

0.8

0.6 ADLeo YZCMi 0.4 EVLac 0.2 EQPeg 0.0 UVCet 0.2 Imag(vis) - 0.3 0.4

0.6 0 30000 60000 90000 120000

Figure 4. Time series of all observations, scaled to a distance of 1 pc. The Stokes I flux√ density is averaged to 10-minute integrations. The frequency bands were chosen to all have the same fractional bandwidth of νmax/νmin ≈ 2. The observations are concatenated, removing times without data, so the x-axis shows the total time on source of our survey. The data are colorized by source, with multiple observations of a source in a given year shown as a continuous block. The time series is the real component of the baseline-averaged visibilities; shown offset by -0.3 Jy (gray line) is the imaginary component of the same quantity, which should not contain stellar signal and thus provides an estimate of the noise in the time series. The red horizontal line shows S1pc =100 mJy, which is used as the minimum threshold flux density for calculating expected transient rates due to stellar coherent radio bursts. COHERENT RADIO BURSTSON MDWARFS 25 almost the entire observed range of frequencies by including responsible for the majority of M dwarf radio transients. To two additional sub-bands, 240-340 MHz and 4-5.6 GHz, but do so, we make a few assumptions: have removed them from the analysis because the Stokes I noise levels in 240-340 MHz were too high to yield mean- 1. The volume density of stellar systems like those in our ingful results, and the coherent bursts at 4-5.6 GHz were too sample is constant with distance. The approximation faint to be detected using our luminosity threshold (which of constant spatial density will break down for estimat- was set by the noise level at 340-480 MHz). ing rates of very faint events, because the density of ac- To measure the coherent burst duty cycle for a given sub- tive M dwarfs declines with height above the galactic band, we must first compute a luminosity time series for all of plane, due to a decline in overall stellar density and our data in that sub-band. For each star, we first convert flux an increase in average stellar age. Increased stellar age means lower activity: the fraction of M4 dwarfs density to a proxy for luminosity, S1pc, which is the flux den- sity of the star scaled to a distance of 1 parsec. We then aver- with magnetic activity declines by about a factor of 2 age the dynamic spectra along the frequency axis to produce at a height of 100 pc above the Galactic plane (West time series, weighting each frequency channel by its inverse et al. 2008). Since our brightest events have S1pc ∼1 Jy, variance. The inverse variance is measured from the imagi- and the assumption of constant volume density of ac- nary component of the dynamic spectrum; this downweights tive mid M dwarfs is good to within a factor of two RFI to maximize sensitivity of the resulting time series. We at 100 pc, we expect that this assumption is not the compute time series of the imaginary component in the same dominant source of error on our estimates of transient fashion, to serve as a control time series that should contain density for flux densities above 0.1 mJy. no stellar bursts. Figure4 shows the resulting time series of The assumption of constant source density as a func- all the survey data. tion of distance means that our predicted transient den- From the time series, we calculate the burst duty cycle, the sities N(> S), as a function of flux density S, will fol- fraction of time that stars spend bursting above a certain lu- low a Euclidean relationship of N(> S) ∝ S −3/2. minosity. We perform this calculation for the time series of 2. Our sample is representative of the active M dwarf the stellar emission, and for the control time series to esti- stellar systems responsible for most radio transients. mate a false alarm rate due to time-variable contamination Our sample consists of single or wide-binary mid- by sidelobes, RFI, and thermal noise. The left panel of Fig- M dwarfs with strong magnetic activity, selected in ure5 shows the burst duty cycle and false alarm rate for part based on their previously-known radio variabil- bursts with S > 100 mJy, corresponding to a luminosity 1pc ity. Active mid-M dwarfs are more prolific sources of of 1.2 × 1014 erg s−1 Hz−1 (assuming isotropic radiation). We radio bursts compared to active early-M dwarfs (e.g., restrict this calculation to a minimum 1-pc flux density of Abada-Simon & Aubier 1997) and are also a more 100 mJy to keep the P band false alarm rate low; this restric- common type of star than earlier-type active M dwarfs, tion does cause some fainter coherent bursts to be neglected, so stars like the ones in our sample should dominate the especially in S band, but we found that using lower thresh- transient population originating from active M dwarfs. old values did not have a major impact on predicted transient However, our burst rate may be skewed by the fact that density, implying that the most luminous events dominate the the majority of our survey time is spent on only two predicted transient population. stars, AD Leo and UV Cet, in only two years; this lim- We find that the coherent burst duty cycle is highest its our ability to account for the variation in activity in the lower half of L band, 1-1.4 GHz, with the tar- properties over time and between stars. get stars producing coherent bursts with S1pc >100 mJy (1.2 × 1014 erg s−1 Hz−1) more than 25% of the time ob- 3. The volume density of M dwarfs producing radio tran- served. Referring to Table3, we find that the duty cycle is sients can be estimated from the number of known highest in this frequency range because bursts are more com- nearby radio-bright M dwarfs. One of the most un- mon, more luminous, and longer duration compared to other certain parts of estimating radio transient rates due to bands. This implies that coherent bursts on active M dwarfs active M dwarfs is the source volume density. Henry will be most significant as a transient source for L band sur- et al.(2018) estimate there are ∼300 stellar systems veys (at least compared to P, S, and C bands, the other bands within 10 pc, in which 75% of stars are M dwarfs 2; considered in this calculation). ∼30% of mid-M dwarfs show magnetic activity in Hα (with a strong dependence on spectral type, 15-50% 6.1.2. Volume Density of Radio-Active M Dwarfs

To predict transient areal density, we need to know the vol- 2 http://www.recons.org/census.posted.htm, accessed on ume density of active M dwarfs, or more specifically, those 2018 Sep 14. 26 VILLADSENETAL. c p

1 0.30 0.12 S Freq (GHz) n

a 0.25 .34-.48 0.10 h t

r 1-1.4 e

t 0.20 1.4-2 0.08 h

g 2-2.8 i r 2.8-4 b 0.15 0.06

e m i

t 0.10 0.04

f o

n 0.05 0.02 o i N(>0.1 mJy) (per sq deg) t c a

r 0.00 0.00 -1 0 F 10 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Flux Density S1pc (Jy) at 1 pc Frequency (GHz)

Figure 5. Frequency dependence of duty cycle and transient density of coherent bursts on active M dwarfs. (left) Fraction of time that a highly active M dwarf, viewed from 1 pc, will be brighter than a given flux density in the listed bands. The thin lines near the bottom show the false alarm rate for each band due to noise, which is near zero above 1.4 GHz. (right) The expected instantaneous density of transients with flux density greater than 0.1 mJy due to stellar coherent radio bursts, as a function of frequency. The width of the horizontal bars shows the frequency range of each band used to calculate transient density. We estimate a factor of 2 systematic uncertainty in transient density (not shown), affecting all frequency bands the same way, due to uncertainty in the volume density of radio-active M dwarfs. for M4 to M6; West et al. 2011), implying a volume than 45% of the active M dwarfs within 10 pc. As- density of stellar systems containing magnetically ac- suming a total of 30-65 (65=30/0.45) radio-active tive M dwarfs of ∼0.016 pc−3. M dwarfs within 10 pc yields a source density of −3 However, the five systems targeted in this survey were 0.007-0.016 pc . chosen for their track record of strong magnetic ac- Our three estimates of source density range from tivity in radio, a more stringent requirement than Hα 0.005-0.016 pc−3. For the following calculations we emission. For purposes of comparison, we calculate use a source density of 0.01 pc−3, with an estimated a lower limit for the volume density of highly radio- factor of 2 uncertainty in transient rate caused by un- active stellar systems based only on our sample: certainty in source density. number of star systems in our sample n = ? volume of our sample 6.1.3. Transient Density 5 We combine the duty cycle of coherent bursts as a function = = 0.005 pc−3. (5) (4/3)π(6.2 pc)3 of luminosity (left panel of Figure5) with the estimated vol- ume density of active M dwarfs to predict a transient density There are a handful of other nearby, fairly well-known due to active M dwarfs. The transient density is the area den- M-dwarf radio emitters that we have not observed, sity (number per square degree on the sky) of sources produc- such as Proxima Cen (Lim et al. 1996; Slee et al. ing coherent bursts above a certain flux density at an instant 2003), CN Leo and Wolf 630 (detected as radio stars in time. The right panel of Figure5 shows, for each sub-band, in e.g., Güdel & Benz 1993). the expected instantaneous transient density N(> S) above For a third estimate counting more radio-active stars S = 0.1 mJy due to active M dwarfs (which can reasonably be beyond those in our sample, we turn to Bower et al. extrapolated to higher flux density thresholds up to ∼10 mJy (2009), who conducted a 5-GHz survey of 104 using N(> S) ∝ S−3/2). As expected based on the high duty M dwarfs within 10 pc, detecting 29 at levels of cycle of coherent bursts at 1-1.4 GHz, the transient density 130 µJy or more. This is roughly 45% of the to- peaks at that frequency, with a density of one >100-µJy tran- tal census of M dwarf stellar systems from Henry sient per 10 square degrees. The transient density declines at et al.(2018), but many of the Bower stars were X- lower and higher frequencies, dropping to only one >100-µJy ray-selected so that the sample likely contains more transient per 300 square degrees for 2.8-4 GHz. The rate of COHERENT RADIO BURSTSON MDWARFS 27 c

p 0 1 0.30 10 S VAST n a 0.25 ThunderKAT h -1 Williams+13

t 10 VLASS r Mooley+16 e

t 0.20

h -2 Bhandari+18

g 10 i r

b 0.15

e -3 10 Polisensky+16 m i

t 0.10 VAST-Wide epoch

f o

-4 VLASS epoch

N(>S) (per sq deg) 10 n 0.05 o i t

c -5 a 0.00 10 r -1 0 -1 0 1 2 3 4 F 10 10 10 10 10 10 10 10

Flux Density S1pc (Jy) at 1 pc Flux Density S (mJy)

Figure 6. Predicted rate of stellar coherent radio bursts in transient surveys. (left) Coherent burst duty cycle, in the style of Figure5, with the exception that the duty cycle is calculated using time series with a shorter integration time of 150 sec. (right) Expected instantaneous transient areal density due to stellar coherent radio bursts (line colors same as left panel). We assume a constant source density as a function of distance, so the predicted transient rates follow a Euclidean relationship of N(> S) ∝ S−3/2. The wedges show a representative flux density detection threshold and measured/predicted 95%-confidence upper limit on transient density for completed/ongoing surveys, colorized by frequency band (black: 0.34 GHz; blue: 1-2 GHz; red: 2-4 GHz): Williams et al.(2013); Mooley et al.(2016); Polisensky et al.(2016); Bhandari et al.(2018); and single epochs of VAST-Wide and VLASS. stellar flares expected for a radio transient survey is therefore sitivity of these bands compared to the 340-480 MHz band highly dependent on the survey’s frequency band. considered in the previous section. Since the majority of our survey’s time focused on two For a given flux density threshold, a survey’s frequency stars, AD Leo and UV Cet, this introduces uncertainty in coverage can have a dramatic effect on instantaneous tran- our predictions of transient density versus radio frequency sient density: for a minimum flux density of 0.1 mJy, we from the entire population of active M dwarfs. The coronae predict a transient density of roughly one per 10 deg2 for of M dwarfs with strong magnetic activity have fairly sim- the VAST and ThunderKAT frequency bands, and one per ilar coronal densities (Table2) and magnetic field strengths 250 deg2 for the VLASS frequency band. The L band sur- (Morin et al. 2008; Reiners et al. 2009), due to coronal satu- veys, VAST and ThunderKAT, will detect a higher density ration (e.g., Wright et al. 2011; Jeffries et al. 2011), implying of stellar coherent radio bursts above a given flux density similar coronal cyclotron and plasma frequencies. However, than the S band survey VLASS because, based on the targets coronal densities and magnetic field strengths are inhomo- and epochs in this paper, the duty cycle of luminous coherent geneous, so bursts may vary in frequency depending where bursts peaks in L band. in the corona they occur in different epochs and on different For comparison, Mooley et al.(2016) use their observa- stars, potentially leading to a broadening of the frequency tions and the literature to predict a ∼1-6 GHz flare star tran- dependence of M dwarf coherent bursts shown in Figure5. sient density of one per 50 deg2 at >0.3 mJy, or one per 10 deg2 at >0.1 mJy, a rate which is higher than their pre- 6.2. Application to Current Transient Surveys dictions for any other type of galactic transient. Their rate, We next calculated the coherent burst duty cycle and ex- which encompasses all types of flare stars including active pected transient density for the frequency bands of three binaries, is comparable to our transient density predictions ongoing or upcoming transient surveys (Figure6): VAST for the L band surveys. Thus, we expect that coherent ra- (1.13-1.43 GHz; Murphy et al. 2013), ThunderKAT L-band dio bursts from active M dwarfs will be among the dominant (0.9-1.67 GHz; but we used 1-1.67 GHz, the part of the sources of galactic transients in the 1-2 GHz band, but not band that overlaps with our frequency coverage), and VLASS at higher frequencies, due to their intrinsically narrowband (2-4 GHz). We generated these predictions following the emission process. same procedure described in the previous section, but using a The total number of transients detected by these surveys shorter integration time of 150 sec, enabled by the better sen- will depend on their single-epoch detection threshold, the 28 VILLADSENETAL. area covered per epoch, and the number of epochs. This in- these events). When surveys reach enough coverage to detect formation is available for VAST (Murphy et al. 2013) and a population of events, rather than 1-2 single events, they will VLASS, so we predict their transient yield due to active reveal whether the stars in this paper are “oddballs” or if their M dwarfs. The VAST survey has multiple sub-surveys with behavior is typical for active mid-M dwarfs. Detection of a different strategies. Here we consider VAST-Wide, which population of events will also make it possible to compare the will cover 10,000 deg2 once per day for 2 years with a per- coherent emission properties of different spectral types, illu- epoch 5σ detection threshold of 2.5 mJy. At this sensitiv- minating the question of what types of star can sustain the ity, we expect a transient density at 1.13-1.43 GHz of 1 per large-scale magnetospheric current systems responsible for 1100 deg2, so VAST-Wide should detect ∼9 coherent radio long-duration coherent bursts. Such detections will identify bursts from active M dwarfs per day. The brightest coherent new targets and categories of star for future targeted stellar bursts in our survey (S1 pc = 1 Jy) can be detected with a flux observations, guiding the search for extrasolar space weather density threshold of 2.5 mJy out to a distance of 20 pc. Us- events. ing our estimated source density of 0.01 pc−3, we can expect about 340 active M dwarf systems to be responsible for these 7. CONCLUSIONS bursts. Assuming a 5σ requirement for VLASS as well gives We have conducted a 58-hour survey of 5 nearby active M a per-epoch detection threshold of 0.6 mJy; VLASS covers dwarfs with the VLA, in order to characterize the frequent 34,000 deg2 in each of 3 epochs. We therefore expect co- coherent radio bursts on these stars and search for events herent radio bursts on active M dwarfs to be responsible for caused by energetic CMEs with radio-loud shock fronts. This ∼10 transients per VLASS epoch. We note again that these survey includes observations from 2013 with continuous cov- predictions are biased by the small number of stars in our erage of 1-6 GHz, and from 2015 with coverage of 0.22-0.48 sample, but we know of no published surveys of transients and 1-4 GHz. This wide bandwidth, enabled by the VLA or radio stars at these low frequencies that have sufficient upgrade, greatly extends the maximum fractional bandwidth sensitivity to overcome the bias introduced by small number of stellar dynamic spectroscopy, opening the possibility of statistics. tracking coronal sources across regions varying by 1-2 orders The right panel of Figure6 shows our predicted transient of magnitude in density or magnetic field strength. areal density as a function of frequency for the frequency We detect frequent coherent bursts in all bands observed, bands of these three surveys. The figure also shows 95% with a total of 22 events occurring across 13 of the 23 epochs. confidence upper limits from a selection of published surveys The events can be very bright, with 9 of the epochs having at frequencies from 0.3-4 GHz (Williams et al. 2013; Moo- a peak flux density above 50 mJy, enabling detailed char- ley et al. 2016; Polisensky et al. 2016; Bhandari et al. 2018), acterization in the time-frequency plane. The properties of and predicted upper limits for VAST-Wide and VLASS sin- the bursts (duration, frequency range, and morphology in gle epochs, assuming no detections were made. Another rel- the time-frequency plane) are very diverse, reflective of the evant transient search, Thyagarajan et al.(2011), used data wide range of dynamic processes occurring in stellar coro- from the VLA FIRST survey at 1.4 GHz to search for tran- nae. The bursts show uniformity only in their high degree of sient/variable sources, detecting 5 radio-variable stars, but circular polarization, in most cases 40-100%, consistent with we do not plot that detection since they do not distinguish the preponderance of active M dwarf coherent bursts in the between types of stars. Figure6 demonstrates that VLASS literature but in contrast to the weak to moderate polariza- and VAST-Wide are among the first radio surveys expected tion observed in many classes of solar coherent bursts. This to systematically detect stellar coherent radio bursts as a tran- strong circular polarization requires the emission to either sient population. be cyclotron maser emission or fundamental plasma emis- Transient surveys will provide an unbiased sample of the sion, and indicates that the depolarization mechanisms oper- population of stellar coherent bursts. Detection of a single ating in the Sun do not strongly affect the coronae of active event offers the potential to trace source motion in a stellar M dwarfs. We divide the bursts into two classes based on du- corona, if the survey has the capability to extract a dynamic ration: short-duration (seconds to minutes) and long-duration spectrum once stellar events are identified; identification and (30 min or more). interpretation of such an event is strengthened by the capabil- The timescale of the short-duration events is consistent ity to measure circular polarization. The scientific return of with the duration of a “space weather” event, such as the such detections can be maximized by rapid follow-up obser- impulsive phase of a flare or a CME crossing the corona. vations, including VLBI (to search for extended structures in We do not detect any clear analogs to solar Type II radio the post-flare radio corona) and lower-frequency radio obser- bursts (associated with CME shock fronts), which may be vations (to search for a low-frequency continuation of space due to: insufficient sensitivity, a CME rate much lower than weather events and for planetary radio emission triggered by expected based on the stellar flare rate, or CMEs failing to COHERENT RADIO BURSTSON MDWARFS 29 form radio-loud shocks due to the high Alfvén speed in ac- sistent on a given star, both in our survey and in the litera- tive M dwarf coronae. In spite of the lack of Type II-like ture from 1977-2015 (albeit with sparse coverage), indicating bursts, frequency drift (which can be caused by moving coro- that these stars have not undergone magnetic reversals on a nal sources) occurs in many bursts on a variety of timescales. timescale of decades. Comparison of the long-duration radio In an exceptional event on YZ CMi, vertical spikes (if due to burst polarization with the orientation of the large-scale mag- unresolved frequency drift) are consistent with source mo- netic field (measured by optical spectropolarimetry) reveals tion at 1.5-15% of the speed of light, with morphological that long-duration bursts are all in the x-mode relative to the resemblance to solar bursts caused by beams of high-speed large-scale field. Due to their strong x-mode polarization, we electrons. The sense of polarization varies with frequency favor the electron cyclotron maser as the emission mecha- in the YZ CMi event, and in general varies between short- nism for long-duration coherent bursts on active M dwarfs. duration events on a given star, pointing to emission from The dependence of polarization on the large-scale field ei- regions with different magnetic polarity, or emission in both ther indicates that the long-duration bursts originate from a x-mode and o-mode. If due to source regions with differ- population of accelerated electrons in the large-scale magne- ent magnetic polarity, this indicates that the short-duration tosphere, analogous to auroral processes on very low mass bursts originate from local phenomena in regions dominated objects, or it can be caused by weak mode coupling. Weak by the small-scale magnetic field (such as flaring in an ac- mode coupling would also help explain the consistent high tive region) rather than from a global magnetospheric pro- degree of circular polarization of active M dwarf radio bursts cess. The short-duration events do not have clear analogs in compared to solar radio bursts, but it faces a challenge in the solar classification system, preventing immediate identifi- the varying sense of polarization of the short-duration bursts, cation of the underlying coronal processes and their potential so we favor instead the interpretation that the long-duration impact on space weather. To identify these phenomena will bursts are caused by a global magnetospheric process. require multi-wavelength data, combined with the diagnostic We find that the coherent burst duty cycle is highest power of wide-bandwidth radio dynamic spectroscopy. Even in the lower half of L band, 1-1.4 GHz, with the tar- without a full understanding of the underlying processes, it get stars producing coherent bursts with S1pc >100 mJy is significant that we do not detect any short-duration bursts (1.2 × 1014 erg s−1 Hz−1) more than 25% of the time ob- that continue beyond our lowest observed frequency. This served. means that we find no evidence of coronal disturbances prop- Long-duration coherent bursts will dominate the popula- agating freely away from active M dwarfs to distances where tion of GHz-frequency transients from active M dwarfs. Due they could impact (hypothetical) planets. Observations with to the intrinsically narrowband nature of coherent emission, deeper sensitivity and/or at lower frequencies can refute or the predicted transient density due to coherent bursts de- strengthen this conclusion. pends strongly on frequency, peaking at 1-1.4 GHz. For The long-duration bursts, which last hours and perhaps this band, the duty cycle of coherent bursts more luminous weeks to months between epochs, require an ongoing elec- than 1.2 × 1014 erg s−1 Hz−1 is just over 25%. We predict a tron acceleration mechanism during the burst. Candidate ac- 1-1.4 GHz transient density of one per 10 deg2, making ac- celeration processes are found within the paradigm of solar tive M dwarfs the most prolific expected source of galactic radio bursts and within the paradigm of periodic radio auro- transients at these frequencies. We use our wideband data rae produced by ultracool dwarfs and planets. Some long- to predict transient densities for the specific frequency bands duration events on AD Leo and YZ CMi show narrow band- of upcoming or ongoing transient surveys, ASKAP’s VAST, width with a sharp lower frequency cutoff, which may be MeerKAT’s ThunderKAT, and the VLA Sky Survey. VAST caused by emission from a closed magnetic structure, analo- and ASKAP’s observations in the 1-2 GHz band should find gous to solar noise storms. However, complex patterns of fre- a high rate of stellar radio bursts from active M dwarfs; we quency drift repeated between epochs on UV Cet point to a predict an active M dwarf transient density for these surveys periodic radio aurora, where the frequency drift is caused by more than an order of magnitude higher than for VLASS. rotational modulation of angularly beamed emission. Angu- Such surveys will identify new targets for study of the global lar beaming may also explain the frequency cutoffs and slow magnetospheric processes probed by long-duration bursts. frequency drift observed on AD Leo. The duration and oc- currence rate of long-duration bursts peak at 1-1.4 GHz com- The authors thank Stephen Bourke for writing the initial pared to both lower and higher frequencies, in contrast to so- version of the tbavg code for producing dynamic spectra in lar radio bursts which become more common below 1 GHz, CASA and for providing guidance on background source indicating that the majority of observed stellar long-duration subtraction, and Michael Eastwood for testing direction- coherent emission originates in the low corona. The sense dependent calibration of our P band data. J.R.V. thanks Tim of polarization of long-duration bursts above 1 GHz is con- Bastian for discussion of stellar radio bursts and feedback on 30 VILLADSENETAL. this paper, Urvashi Rao for imaging advice, and Rick Perley made use of the SIMBAD database, operated at CDS, Stras- and Frank Schinzel for help with P band polarization cal- bourg, France. This research has made us of NASA’s Astro- ibration. The authors thank the referee for thoughtful and physics Data System. This research made use of Astropy, a constructive feedback. community-developed core Python package for Astronomy. This material is based upon work supported by the Na- The acknowledgements were compiled using the Astronomy tional Science Foundation under Grant No. AST-1311098. Acknowledgement Generator. J.R.V. additionally thanks the Troesh family and the PEO In- Facilities: VLA ternational Scholar Award program for financial support of her graduate research. Software: CASA, Astropy (Astropy Collaboration et al. The National Radio Astronomy Observatory is a facility of 2013), Anaconda, SIMBAD, ADS, NumPy (Van Der Walt the National Science Foundation operated under cooperative et al. 2011), SciPy (Jones et al. 2001), Matplotlib (Hunter agreement by Associated Universities, Inc. This research has 2007)

REFERENCES

Aarnio, A. N., Matt, S. P., & Stassun, K. G. 2012, ApJ, 760, 9 Benz, A., ed. 2002, Astrophysics and Space Science Library, Vol. Aarnio, A. N., Stassun, K. G., Hughes, W. J., & McGregor, S. L. 279, Plasma Astrophysics, second edition 2011, SoPh, 268, 195 Benz, A. O., Conway, J., & Güdel, M. 1998, A&A, 331, 596 Abada-Simon, M., & Aubier, M. 1997, A&AS, 125 Benz, A. O., & Güdel, M. 1994, A&A, 285, 621 Abdul-Aziz, H., Abranin, E. P., Alekseev, I. Y., et al. 1995, A&AS, Benz, A. O., Jaeggi, M., & Zlobec, P. 1982, A&A, 109, 305 114, 509 Benz, A. O., Magun, A., Stehling, W., & Su, H. 1992, SoPh, 141, Abranin, E. P., Alekseev, I. Y., Avgoloupis, S., et al. 1998, 335 Astronomical and Astrophysical Transactions, 17, 221 Benz, A. O., & Thejappa, G. 1988, A&A, 202, 267 Airapetian, V. S., Glocer, A., Gronoff, G., Hébrard, E., & Danchi, Berdyugina, S. V., Harrington, D. M., Kuzmychov, O., et al. 2017, W. 2016, Nature Geoscience, 9, 452 ApJ, 847, 61 Airapetian, V. S., & Holman, G. D. 1998, ApJ, 501, 805 Bhandari, S., Bannister, K. W., Murphy, T., et al. 2018, MNRAS, 478, 1784 Allen, C. W. 1947, MNRAS, 107, 426 Boccaletti, A., Thalmann, C., Lagrange, A.-M., et al. 2015, Nature, Alvarado-Gómez, J. D., Drake, J. J., Cohen, O., Moschou, S. P., & 526, 230 Garraffo, C. 2018, ArXiv e-prints, arXiv:1806.02828 Bond, H. E., Mullan, D. J., O’Brien, M. S., & Sion, E. M. 2001, [astro-ph.SR] ApJ, 560, 919 Ambruster, C. W., Pettersen, B. R., Hawley, S., Coleman, L. A., & Bonfils, X., Astudillo-Defru, N., Díaz, R., et al. 2017, ArXiv Sandmann, W. H. 1986, in ESA Special Publication, Vol. 263, e-prints, arXiv:1711.06177 [astro-ph.EP] New Insights in Astrophysics. Eight Years of UV Astronomy Bower, G. C., Bolatto, A., Ford, E. B., & Kalas, P. 2009, ApJ, 701, with IUE, ed. E. J. Rolfe 1922 Anglada-Escudé, G., Amado, P. J., Barnes, J., et al. 2016, Nature, Cane, H. V., Sheeley, Jr., N. R., & Howard, R. A. 1987, 536, 437 J. Geophys. Res., 92, 9869 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, Chen, B., Bastian, T. S., White, S. M., et al. 2013, ApJL, 763, L21 A&A, 558, A33 Cho, K.-S., Gopalswamy, N., Kwon, R.-Y., Kim, R.-S., & Yashiro, Atri, D. 2017, MNRAS, 465, L34 S. 2013, ApJ, 765, 148 Audard, M., Güdel, M., & Skinner, S. L. 2003, ApJ, 589, 983 Cliver, E. W., Ling, A. G., Belov, A., & Yashiro, S. 2012, ApJL, Barnes, J. R., Jeffers, S. V., Haswell, C. A., et al. 2017, MNRAS, 756, L29 471, 811 Collier Cameron, A., & Robinson, R. D. 1989, MNRAS, 238, 657 Bastian, T. S. 1990, SoPh, 130, 265 Cranmer, S. R. 2017, ApJ, 840, 114 Bastian, T. S., Benz, A. O., & Gary, D. E. 1998, ARA&A, 36, 131 Crosley, M. K., & Osten, R. A. 2018a, ApJ, 856, 39 Bastian, T. S., Bookbinder, J., Dulk, G. A., & Davis, M. 1990, ApJ, —. 2018b, ApJ, 862, 113 353, 265 Crosley, M. K., Osten, R. A., & Norman, C. 2017, ApJ, 845, 67 Belov, A., Kurt, V., Mavromichalaki, H., & Gerontidou, M. 2007, Crosley, M. K., Osten, R. A., Broderick, J. W., et al. 2016, ApJ, SoPh, 246, 457 830, 24 Bentley, R. D., Klein, K.-L., van Driel-Gesztelyi, L., et al. 2000, Cully, S. L., Fisher, G. H., Abbott, M. J., & Siegmund, O. H. W. SoPh, 193, 227 1994, ApJ, 435, 449 COHERENT RADIO BURSTSON MDWARFS 31

Das, B., Chandra, P., & Wade, G. A. 2018, MNRAS, 474, L61 Hess, S., Cecconi, B., & Zarka, P. 2008, Geophys. Res. Lett., 35, Davis, R. J., Lovell, B., Palmer, H. P., & Spencer, R. E. 1978, L13107 Nature, 273, 644 Hey, J. S. 1946, Nature, 157, 47 Drake, J. J., Cohen, O., Yashiro, S., & Gopalswamy, N. 2013, ApJ, Houdebine, E. R., Foing, B. H., & Rodono, M. 1990, A&A, 238, 764, 170 249 Dressing, C. D., & Charbonneau, D. 2015, ApJ, 807, 45 Howard, W. S., Tilley, M. A., Corbett, H., et al. 2018, ArXiv Dulk, G. A. 1985, ARA&A, 23, 169 e-prints, arXiv:1804.02001 [astro-ph.EP] Dulk, G. A., & Suzuki, S. 1980, A&A, 88, 203 Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90 Elgarøy, E. Ø. 1977, Solar noise storms. Intema, H. T., van der Tol, S., Cotton, W. D., et al. 2009, A&A, Favata, F., & Schmitt, J. H. M. M. 1999, A&A, 350, 900 501, 1185 France, K., Parke Loyd, R. O., Youngblood, A., et al. 2016, ApJ, Jackson, P. D., Kundu, M. R., & Kassim, N. 1990, SoPh, 130, 391 820, 89 Jaeggi, M., & Benz, A. O. 1982, A&A, 107, 88 Fuhrmeister, B., & Schmitt, J. H. M. M. 2004, A&A, 420, 1079 Jeffries, R. D., Jackson, R. J., Briggs, K. R., Evans, P. A., & Pye, Gagné, M., Valenti, J., Johns-Krull, C., et al. 1998, in Ast. Soc. of J. P. 2011, MNRAS, 411, 2099 the Pac. Conference Series, Vol. 154, Cool Stars, Stellar Jones, E., Oliphant, T., Peterson, P., & Others. 2001, SciPy: Open Systems, and the Sun, ed. R. A. Donahue & J. A. Bookbinder, source scientific tools for Python 1484 Kahler, S., Golub, L., Harnden, F. R., et al. 1982, ApJ, 252, 239 Giles, H. A. C., Collier Cameron, A., & Haywood, R. D. 2017, Kaiser, M. L., Zarka, P., Kurth, W. S., Hospodarsky, G. B., & MNRAS, 472, 1618 Gurnett, D. A. 2000, J. Geophys. Res., 105, 16053 Gillon, M., Triaud, A. H. M. J., Demory, B.-O., et al. 2017, Nature, Katsova, M. M., Drake, J. J., & Livshits, M. A. 1999, ApJ, 510, 986 542, 456 Kay, C., Opher, M., & Kornbleuth, M. 2016, ApJ, 826, 195 Gopalswamy, N., Lara, A., Kaiser, M. L., & Bougeret, J.-L. 2001, Kellett, B. J., Bingham, R., Cairns, R. A., & Tsikoudi, V. 2002, J. Geophys. Res., 106, 25261 MNRAS, 329, 102 Gopalswamy, N., Thompson, W. T., Davila, J. M., et al. 2009, Kervella, P., Mérand, A., Ledoux, C., Demory, B.-O., & Le SoPh, 259, 227 Bouquin, J.-B. 2016, ArXiv e-prints, arXiv:1607.04351 Güdel, M. 1994, ApJS, 90, 743 [astro-ph.SR] Güdel, M. 2002, ARA&A, 40, 217 Khodachenko, M. L., Ribas, I., Lammer, H., et al. 2007, Güdel, M., Audard, M., Kashyap, V. L., Drake, J. J., & Guinan, Astrobiology, 7, 167 E. F. 2003, ApJ, 582, 423 Kochukhov, O., & Lavail, A. 2017, ApJL, 835, L4 Güdel, M., & Benz, A. O. 1990, A&A, 231, 202 Komesaroff, M. 1958, Australian Journal of Physics, 11, 201 —. 1993, ApJL, 405, L63 Kouloumvakos, A., Nindos, A., Valtonen, E., et al. 2015, A&A, Güdel, M., Benz, A. O., Schmitt, J. H. M. M., & Skinner, S. L. 580, A80 1996, ApJ, 471, 1002 Kowalski, A. F., Hawley, S. L., Holtzman, J. A., Wisniewski, J. P., Güdel, M., Guinan, E. F., & Skinner, S. L. 1997, ApJ, 483, 947 & Hilton, E. J. 2010, ApJL, 714, L98 Guhathakurta, M., Fludra, A., Gibson, S. E., Biesecker, D., & Kowalski, A. F., Hawley, S. L., Wisniewski, J. P., et al. 2013, Fisher, R. 1999, J. Geophys. Res., 104, 9801 ApJS, 207, 15 Haisch, B. M., Linsky, J. L., Bornmann, P. L., et al. 1983, ApJ, Kumari, A., Ramesh, R., Kathiravan, C., & Gopalswamy, N. 2017, 267, 280 ApJ, 843, 10 Hallinan, G., Antonova, A., Doyle, J. G., et al. 2008, ApJ, 684, 644 Kundu, M. R., White, S. M., Jackson, P. D., & Pallavicini, R. 1988, Hallinan, G., Bourke, S., Lane, C., et al. 2007, ApJL, 663, L25 A&A, 195, 159 Hallinan, G., Littlefair, S. P., Cotter, G., et al. 2015, Nature, 523, Lacy, C. H., Moffett, T. J., & Evans, D. S. 1976, ApJS, 30, 85 568 Lammer, H., Lichtenegger, H. I. M., Kulikov, Y. N., et al. 2007, Harra, L. K., Schrijver, C. J., Janvier, M., et al. 2016, SoPh, 291, Astrobiology, 7, 185 1761 Lang, K. R., & Willson, R. F. 1986, ApJL, 302, L17 Havnes, O., & Goertz, C. K. 1984, A&A, 138, 421 —. 1988, ApJ, 326, 300 Hawley, S. L., & Pettersen, B. R. 1991, ApJ, 378, 725 Lecavelier des Etangs, A., Bourrier, V., Wheatley, P. J., et al. 2012, Heintz, W. D. 1984, AJ, 89, 1063 A&A, 543, L4 Henry, T. J., Kirkpatrick, J. D., & Simons, D. A. 1994, AJ, 108, Lefèvre, E., Klein, K.-L., & Lestrade, J.-F. 1994, A&A, 283, 483 1437 Leitzinger, M., Odert, P., Greimel, R., et al. 2014, MNRAS, 443, Henry, T. J., Jao, W.-C., Winters, J. G., et al. 2018, AJ, 155, 265 898 32 VILLADSENETAL.

Leitzinger, M., Odert, P., Ribas, I., et al. 2011, A&A, 536, A62 Newton, E. R., Irwin, J., Charbonneau, D., et al. 2016, ApJ, 821, 93 Lenc, E., Murphy, T., Lynch, C. R., Kaplan, D. L., & Zhang, S. N. Nita, G. M., Gary, D. E., Lanzerotti, L. J., & Thomson, D. J. 2002, 2018, MNRAS, 478, 2835 ApJ, 570, 423 Liefke, C., Ness, J.-U., Schmitt, J. H. M. M., & Maggio, A. 2008, Nonino, M., Comari, M., Zlobec, P., Abrami, A., & Messerotti, M. A&A, 491, 859 1986, SoPh, 104, 111 Lim, J., White, S. M., & Slee, O. B. 1996, ApJ, 460, 976 Noordam, J. E. 2004, in Proc. SPIE, Vol. 5489, Ground-based Linsky, J. L., Drake, S. A., & Bastian, T. S. 1992, ApJ, 393, 341 Telescopes, ed. J. M. Oschmann, Jr., 817 Lovell, B. 1963, Nature, 198, 228 Obenberger, K. S., Taylor, G. B., Hartman, J. M., et al. 2015, Lynch, C. R., Lenc, E., Kaplan, D. L., Murphy, T., & Anderson, Journal of Astronomical Instrumentation, 4, 1550004 G. E. 2017, ApJL, 836, L30 Odert, P., Leitzinger, M., Hanslmeier, A., & Lammer, H. 2017, Magdalenic,´ J., Marqué, C., Zhukov, A. N., Vršnak, B., & Veronig, MNRAS, 472, 876 A. 2012, ApJ, 746, 152 Orchiston, W. 2005, Journal of Astronomical History and Heritage, Maggio, A., Drake, J. J., Kashyap, V., et al. 2004, ApJ, 613, 548 8, 3 Mann, A. W., Feiden, G. A., Gaidos, E., Boyajian, T., & von Osten, R., Livio, M., Lubow, S., et al. 2013, ApJL, 765, L44 Braun, K. 2015, ApJ, 804, 64 Osten, R. A. 2008, in POS Dynamic, Vol. 005, Proceedings from Mann, G., Classen, T., & Aurass, H. 1995, A&A, 295, 775 "Bursts, Pulses and Flickering: Wide-field Monitoring of the Mann, G., Klassen, A., Aurass, H., & Classen, H.-T. 2003, A&A, Dynamic Radio Sky" 400, 329 Osten, R. A., & Bastian, T. S. 2006, ApJ, 637, 1016 Mason, J. P., Woods, T. N., Caspi, A., Thompson, B. J., & Hock, —. 2008, ApJ, 674, 1078 R. A. 2014, ApJ, 789, 61 Osten, R. A., Hawley, S. L., Allred, J., et al. 2006, ApJ, 647, 1349 McMullin, J. P., Waters, B., Schiebel, D., Young, W., & Golap, K. Osten, R. A., Hawley, S. L., Allred, J. C., Johns-Krull, C. M., & 2007, in Ast. Soc. of the Pac. Conference Series, Vol. 376, Roark, C. 2005, ApJ, 621, 398 Astronomical Data Analysis Software and Systems XVI, ed. Osten, R. A., & Wolk, S. J. 2015, ApJ, 809, 79 R. A. Shaw, F. Hill, & D. J. Bell, 127 Patsourakos, S., & Georgoulis, M. K. 2017, SoPh, 292, 89 Mellott, M. M., Huff, R. L., & Gurnett, D. A. 1986, Payne-Scott, R., Yabsley, D. E., & Bolton, J. G. 1947, Nature, 160, J. Geophys. Res., 91, 13732 256 Melrose, D. B. 1980, SoPh, 67, 357 Peres, G., Orlando, S., Reale, F., Rosner, R., & Hudson, H. 2000, —. 1991, ARA&A, 29, 31 ApJ, 528, 537 —. 1994, SSRv, 68, 159 Perley, R. A., & Butler, B. J. 2013, ApJS, 204, 19 Melrose, D. B., & Dulk, G. A. 1982, ApJ, 259, 844 —. 2017, ApJS, 230, 7 Melrose, D. B., Dulk, G. A., & Hewitt, R. G. 1984, Polisensky, E., Lane, W. M., Hyman, S. D., et al. 2016, ApJ, 832, J. Geophys. Res., 89, 897 60 Melrose, D. B., Dulk, G. A., & Smerd, S. F. 1978, A&A, 66, 315 Prakash, O., Feng, L., Michalek, G., et al. 2017, Ap&SS, 362, 56 Mooley, K. P., Hallinan, G., Bourke, S., et al. 2016, ApJ, 818, 105 Prakash, O., Umapathy, S., Shanmugaraju, A., Pappa Kalaivani, P., Morin, J., Donati, J.-F., Petit, P., et al. 2008, MNRAS, 390, 567 Morosan, D. E., Zucca, P., Bloomfield, D. S., & Gallagher, P. T. & Vršnak, B. 2010, SoPh, 266, 135 2016, A&A, 589, L8 Prasad, P., Huizinga, F., Kooistra, E., et al. 2016, Journal of Murphy, T., Chatterjee, S., Kaplan, D. L., et al. 2013, PASA, 30, Astronomical Instrumentation, 5, 1641008 e006 Raassen, A. J. J., Mitra-Kraev, U., & Güdel, M. 2007, MNRAS, Murphy, T., Kaplan, D. L., Croft, S., et al. 2017, MNRAS, 466, 379, 1075 1944 Rau, U., & Cornwell, T. J. 2011, A&A, 532, A71 Nelson, G. J., & Melrose, D. B. 1985, Type II bursts, ed. D. J. Reames, D. V. 2013, SSRv, 175, 53 McLean & N. R. Labrum, 333 Reiners, A., & Basri, G. 2007, ApJ, 656, 1121 Nelson, G. J., Robinson, R. D., Slee, O. B., et al. 1986, MNRAS, —. 2009, A&A, 496, 787 220, 91 Reiners, A., Basri, G., & Browning, M. 2009, ApJ, 692, 538 Ness, J.-U., Güdel, M., Schmitt, J. H. M. M., Audard, M., & Roberts, J. A. 1959, Australian Journal of Physics, 12, 327 Telleschi, A. 2004, A&A, 427, 667 Route, M. 2016, ApJL, 830, L27 Ness, J.-U., Mewe, R., Schmitt, J. H. M. M., et al. 2001, A&A, Saito, K., Makita, M., Nishi, K., & Hata, S. 1970, Annals of the 367, 282 Tokyo Astronomical Observatory, 12, 53 Newkirk, Jr., G. 1967, ARA&A, 5, 213 Scaife, A. M. M., & Heald, G. H. 2012, MNRAS, 423, L30 COHERENT RADIO BURSTSON MDWARFS 33

Segura, A., Walkowicz, L. M., Meadows, V., Kasting, J., & Van Der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Hawley, S. 2010, Astrobiology, 10, 751 Computing in Science & Engineering, 13, 22 Shields, A. L., Ballard, S., & Johnson, J. A. 2016, ArXiv e-prints, Vida, K., Kriskovics, L., Oláh, K., et al. 2016, A&A, 590, A11 arXiv:1610.05765 [astro-ph.EP] Vidotto, A. A., Donati, J.-F., Jardine, M., et al. 2016, MNRAS, Shkolnik, E., Liu, M. C., & Reid, I. N. 2009, ApJ, 699, 649 455, L52 Shulyak, D., Reiners, A., Seemann, U., Kochukhov, O., & Vršnak, B., & Cliver, E. W. 2008, SoPh, 253, 215 Piskunov, N. 2014, A&A, 563, A35 West, A. A., Hawley, S. L., Bochanski, J. J., et al. 2008, AJ, 135, Slee, O. B., Willes, A. J., & Robinson, R. D. 2003, PASA, 20, 257 Smerd, S. F. 1976, SoPh, 46, 493 785 Southworth, G. C. 1945, Microwave Radiation from the Sun (with West, A. A., Morgan, D. P., Bochanski, J. J., et al. 2011, AJ, 141, Erratum), ed. W. T. Sullivan, III, 168 97 Spangler, S. R., & Moffett, T. J. 1976, ApJ, 203, 497 White, S. M., Kundu, M. R., & Jackson, P. D. 1986, ApJ, 311, 814 Staehli, M., & Magun, A. 1986, SoPh, 104, 117 Williams, P. K. G., Bower, G. C., Croft, S., et al. 2013, ApJ, 762, Stepanov, A. V., Kliem, B., Zaitsev, V. V., et al. 2001, A&A, 374, 85 1072 Winglee, R. M. 1985, J. Geophys. Res., 90, 9663 Stewart, A. J., Fender, R. P., Broderick, J. W., et al. 2016, MNRAS, Wood, B. E., Laming, J. M., Warren, H. P., & Poppenhaeger, K. 456, 2321 2018, ArXiv e-prints, arXiv:1806.05111 [astro-ph.SR] Stewart, R. T., Brueckner, G. E., & Dere, K. P. 1986, SoPh, 106, 107 Wood, B. E., Müller, H.-R., Zank, G. P., Linsky, J. L., & Redfield, Su, W., Cheng, X., Ding, M. D., Chen, P. F., & Sun, J. Q. 2015, S. 2005, ApJL, 628, L143 ApJ, 804, 88 Wright, N. J., Drake, J. J., Mamajek, E. E., & Henry, G. W. 2011, Sun, X., Bobra, M. G., Hoeksema, J. T., et al. 2015, ApJL, 804, ApJ, 743, 48 L28 Yashiro, S., Akiyama, S., Gopalswamy, N., & Howard, R. A. 2006, Thalmann, J. K., Su, Y., Temmer, M., & Veronig, A. M. 2015, ApJL, 650, L143 ApJL, 801, L23 Yashiro, S., & Gopalswamy, N. 2009, in IAU Symposium, Vol. Thejappa, G., MacDowall, R. J., & Bergamo, M. 2012, ApJ, 745, 257, Universal Heliophysical Processes, ed. N. Gopalswamy & 187 D. F. Webb, 233 Thejappa, G., Zlobec, P., & MacDowall, R. J. 2003, ApJ, 592, 1234 Youngblood, A., France, K., Parke Loyd, R. O., et al. 2017, ApJ, Thyagarajan, N., Helfand, D. J., White, R. L., & Becker, R. H. 843, 31 2011, ApJ, 742, 49 Tilley, M. A., Segura, A., Meadows, V. S., Hawley, S., & Zarka, P. 1998, J. Geophys. Res., 103, 20159 Davenport, J. 2017, ArXiv e-prints, arXiv:1711.08484 Za˘itsev, V. V., Shaposhnikov, V. E., & Rucker, H. O. 2005, [astro-ph.EP] Astronomy Reports, 49, 327 Treumann, R. A. 2006, A&A Rv, 13, 229 Zhao, G. Q., Feng, H. Q., & Wu, D. J. 2016, Physics of Plasmas, Trigilio, C., Leto, P., Umana, G., Buemi, C. S., & Leone, F. 2011, 23, 052109 ApJL, 739, L10 Zlobec, P., Messerotti, M., Karlicky, M., & Urbarz, H. 1993, SoPh, van den Oord, G. H. J., Doyle, J. G., Rodono, M., et al. 1996, 144, 373 A&A, 310, 908 34 VILLADSENETAL.

APPENDIX

A. DISTINGUISHING STELLAR BURSTS AND ARTIFACTS IN THE DYNAMIC SPECTRUM Figure7 shows an example of the different data products used to identify radio bursts and characterize noise levels in the dynamic spectrum. The dynamic spectrum is the real component of the baseline-averaged visibilities (broken down into separate polarizations, e.g., Stokes I and V), which contains the emission from the star at the phase center. Sources of noise and artifacts include: thermal noise, RFI, and residual sidelobes from imperfectly-subtracted background sources. None of the sources of noise and artifacts are located at the phase center, with the result that they produce striation patterns in the dynamic spectrum (alternating between positive/red and negative/blue), and they also produce a signal in the imaginary component of the baseline- averaged visibilities. In contrast, the target star (a point source at the phase center) only produces emission in the real component of the baseline-averaged visibilities, with no contribution to the imaginary component. In AppendixB, we present dynamic spectra of detected bursts, showing only the real component of the baseline-averaged visibilities, but the imaginary component of the baseline-averaged visibilities has been inspected as well for each event; these imaginary-component dynamic spectra are included as figures, identical in format to those in AppendixB, in this paper’s online supplementary files. The stellar origin of a number of bursts has been confirmed by imaging. In the absence of noise, stellar emission in the Stokes I dynamic spectrum is always positive (red), and in Stokes V the stellar emission consists of continuous patches of right-polarized emission (positive values; a clump of red pixels) and/or left-polarized emission (negative values; a clump of blue pixels). In Figure7, a left-polarized stellar burst is present throughout the entire duration in the Stokes I and V dynamic spectra (1st and 3rd panels from left) at 1.1-1.6 GHz. (There is also fainter broadband left-polarized stellar emission present throughout the entire frequency range and duration.) Horizontal white gaps indicate frequency ranges that have been entirely flagged due to RFI; vertical white gaps are time intervals with no data due to calibrator observations. Other features in the figure provide examples of different types of noise/artifacts:

• Thermal noise. The imaginary component of the baseline-averaged visibilities for Stokes V (bottom right panel) is dom- inated by thermal noise at most frequencies. Thermal noise appears in the dynamic spectrum as random variation that is not correlated across adjacent pixels, with values centered around zero (so thermal noise does not introduce a systematic offset in the average flux density).

• RFI. The same panel shows the effect of RFI at ∼1.5 GHz. The heightened intensity at this frequency is due to 2 effects: 1) RFI signals (which can produce noise that is correlated across multiple pixels), and 2) increased thermal noise levels because certain baselines with strong RFI have been flagged at these frequencies. The fact that this feature is seen in the imaginary component of the baseline-averaged visibilities (unlike stellar emission), along with the alternation between positive and negative values, demonstrates that it is not at the phase center and not of stellar origin (which can be confirmed by imaging the affected time and frequency range). We did not completely flag all frequency ranges affected by RFI since it would remove a significant fraction of our observing band, and because certain stellar bursts are detected in these RFI-contaminated ranges (in these cases, the stellar origin of the burst has been confirmed by imaging).

• Residual sidelobes. Residuals after background source subtraction affect Stokes I but do not significantly affect Stokes V, due to the absence of circularly polarized background sources. This can be seen in the imaginary component of the baseline- averaged Stokes I visibilities (top right panel), as alternating positive and negative “wiggles” in the time-frequency plane. These wiggles are most intense at the lowest frequencies, which have numerous bright background sources and a wide field of view. The effect of background sources in the Stokes I dynamic spectrum (top left panel) is to introduce low level variations in the structure of the stellar emission across the dynamic spectrum. These variations are not seen in the Stokes V dynamic spectrum, so at low frequencies Stokes V provides a more accurate picture of fine structure in stellar radio bursts.

To avoid interpreting artifacts as stellar bursts, the imaginary component of the baseline-averaged visibilities was inspected for each event while interpreting the dynamic spectrum. The noise levels in each frequency channel were measured using the standard deviation across time of the imaginary component in that channel, a quantity that accounts for the effects of all 3 types of artifacts (thermal noise, RFI, and residual sidelobes). The approach of measuring noise levels across multiple pixels of the imaginary component of the baseline-averaged visibilities is used throughout this work, used as a way to assess the significance of bursts (Section 3.3), to conduct a weighted average of dynamic spectra to produce time series (Section6), and to determine the errors on peak flux density, degree of circular polarization, and energy quoted in Table3. COHERENT RADIO BURSTSON MDWARFS 35

Stokes I Imag(I)

3.5

3.0

2.5

2.0

1.5

0.0 60.0 120.0 180.0 0.0 60.0 120.0 180.0

Stokes V Imag(V) 15.0 Frequency (GHz)

3.5

7.5 3.0

2.5 0.0

2.0

-7.5 Flux Density (mJy) 1.5

-15.0 0.0 60.0 120.0 180.0 0.0 60.0 120.0 180.0 Time (min) since 2015-07-05 20:59:21 UT

Figure 7. Example of data products used to identify radio bursts. All panels are 1-4 GHz dynamic spectra of a 4-hour observation of AD Leo, binned to a resolution of 32 MHz and 60 sec. (top left) Stokes I dynamic spectrum of the target, generated by averaging the Stokes I visibilities over all baselines and taking the real component. All stellar Stokes I flux density should be positive, or red. (top right) Imaginary component of the baseline-averaged Stokes I visibilities. No signal from the target star at the phase center appears in the imaginary component, so this spectrum provides an estimate of noise levels due to thermal noise, RFI, and residuals of background sources. (bottom left) Stokes V dynamic spectrum of the target. Right circular polarization is positive/red, and left is negative/blue. (bottom right) Imaginary component of the baseline- averaged Stokes V visibilities. Stokes V has lower noise levels than Stokes I, due to the absence of circularly polarized background sources. 36 VILLADSENETAL.

B. DYNAMIC SPECTRA OF ALL RADIO BURSTS Figures 8d-8m show the dynamic spectra from all epochs with detected radio bursts. All epochs are shown with the same scale in time and frequency (i.e., hours per inch and GHz per inch) but with different binning and color scales to highlight the features in each epoch.

EQ Peg - 2015-05-16 Stokes I, 1-4 GHz Stokes V, 1-4 GHz

3.5 3.5 10

3.0 3.0

2.5 2.5 0

2.0 2.0 1-4 Flux Density (mJy)

-10 1.5 1.5

0.0 30.0 60.0 90.0 0.0 30.0 60.0 90.0

Frequency (GHz) Stokes I, 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 100 0.45 0.45 0.4 0.4 0.35 0.35 50 0.3 0.3 0.25 0.25 0.0 30.0 60.0 90.00.0 30.0 60.0 90.0 0 Stokes U', 0.2-0.5 GHz 0.45 0.4 -50 0.35 0.3 0.25 -100 0.2-0.5 GHz Flux Density (mJy) 0.0 30.0 60.0 90.0 Time (min) since 2015-05-16 14:29:21 UT

Figure 8a. Dynamic spectra of the 2-hour observation of EQ Peg on 2015 May 16. The left column shows the Stokes I dynamic spectrum, with different color scales and binning for 1-4 GHz (top) and 0.2-0.5 GHz (bottom). The right column shows the Stokes V dynamic spectrum. For 0.2-0.5 GHz, we show both Stokes V’ and U’, using the ’ symbol to denote that cross-hand phase has not been corrected for this frequency band, such that the true Stokes V has undergone an arbitrary rotation between V’ and U’. In this epoch, we identify two coherent bursts, distinct spectral features that overlap in time: a broadband right-polarized event at 1-3 GHz for the first 30+ minutes, and a narrowband strongly polarized event at 0.35-0.385 GHz for the first 35 minutes. Since the low-frequency event occurs at RFI-contaminated frequencies, we verified its stellar origin by imaging the star during the burst, detecting it with flux density 31.3±6.4 (I), -25.9±3.9 (U’), and -12.1±4.3 (V’). COHERENT RADIO BURSTSON MDWARFS 37

YZ CMi - 2015-05-11 Stokes I, 1-4 GHz Stokes V, 1-4 GHz 50.0 33.3

3.5 3.5 16.7

3.0 3.0

2.5 2.5 -0.0

2.0 2.0 1-4 Flux Density (mJy)

1.5 1.5 -16.7

-33.3 -50.0 0.0 30.0 60.0 90.00.0 30.0 60.0 90.0

Frequency (GHz) Stokes I, 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 50 0.45 0.45 0.4 0.4 0.35 0.35 25 0.3 0.3 0.25 0.25 0.0 30.0 60.0 0.0 30.0 60.0 0 Stokes U', 0.2-0.5 GHz 0.45 0.4 -25 0.35 0.3

0.25 0.2-0.5 GHz Flux Density (mJy) -50 0.0 30.0 60.0 Time (min) since 2015-05-11 23:36:14 UT

Figure 8b. Dynamic spectra of the 2-hour observation of YZ CMi on 2015 May 11, in the style of Figure 8a. In this epoch, we identify two coherent bursts, which overlap in time but are distinct spectral features: a short-duration event with complex polarization structure at 1-3.7 GHz at t∼60-70 min, and long-duration left-polarized emission throughout the observation at 3-3.7 GHz. This epoch is shown using matplotlib’s “symlog” scale (linear near the origin, logarithmic at large flux densities) in order to highlight events at a range of intensities. The color scale and binning are chosen to make the long-duration emission visible, and the short-duration event is shown in greater detail in Figure 1a. 38 VILLADSENETAL.

YZ CMi - 2015-05-13 Stokes I, 1-4 GHz Stokes V, 1-4 GHz 15.0

3.5 3.5

7.5

3.0 3.0

2.5 2.5 0.0

2.0 2.0 1-4 Flux Density (mJy) -7.5

1.5 1.5

-15.0 0.0 30.0 60.0 90.0 0.0 30.0 60.0 90.0

Frequency (GHz) Stokes I, 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 50 0.45 0.45 0.4 0.4 0.35 0.35 25 0.3 0.3 0.25 0.25 0.0 30.0 60.0 0.0 30.0 60.0 0 Stokes U', 0.2-0.5 GHz 0.45 0.4 -25 0.35 0.3

0.25 0.2-0.5 GHz Flux Density (mJy) -50 0.0 30.0 60.0 Time (min) since 2015-05-13 00:32:30 UT

Figure 8c. Dynamic spectra of the 2-hour observation of YZ CMi on 2015 May 13, in the style of Figure 8a. In this epoch, we identify one coherent burst, a long-duration event from 2-2.7 GHz lasting at least 45 minutes. COHERENT RADIO BURSTSON MDWARFS 39

Frequency (GHz) 0.25 0.35 0.45 0.3 0.4 1.5 2.0 2.5 3.0 3.5 0.0 0.0 60.0 60.0 Stokes I, 0.2-0.5 GHz Stokes I, 1-4 GHz 120.0 120.0 Time (min) since 2015-07-05 20:58:20 UT 180.0 180.0 AD Leo - 2015-07-05 0.0 0.0 0.0 60.0 Stokes U', 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 60.0 60.0 Stokes V, 1-4 GHz 120.0 120.0 120.0 180.0 180.0 180.0 0.25 0.3 0.35 0.4 0.45 0.25 0.3 0.35 0.4 0.45 1.5 2.0 2.5 3.0 3.5 -20 -10 0 10 20 -30 -15 0 15 30

0.2-0.5 GHz Flux Density (mJy) 1-4 Flux Density (mJy) Figure 8d. Dynamic spectra of the 4-hour observation of AD Leo on 2015 July 5, in the style of Figure 8a. In this epoch, we identify two coherent bursts: both long-duration events lasting throughout the observation, one at 1.1-1.6 GHz, and one at 0.28-0.4 GHz. While these events occur at the same time, we identify them as separate events since they are distinct spectral features and because the 1.1-1.6 GHz emission recurs without the lower-frequency component on 2015 July 19 (Figure 8e). 40 VILLADSENETAL.

Frequency (GHz) 0.25 0.35 0.45 0.3 0.4 1.5 2.0 2.5 3.0 3.5 0.0 0.0 60.0 60.0 Stokes I, 0.2-0.5 GHz Stokes I, 1-4 GHz 120.0 120.0 Time (min) since 2015-07-19 20:03:12 UT 180.0 180.0 AD Leo - 2015-07-19 0.0 0.0 0.0 60.0 Stokes U', 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 60.0 60.0 Stokes V, 1-4 GHz 120.0 120.0 120.0 180.0 180.0 180.0 0.25 0.3 0.35 0.4 0.45 0.25 0.3 0.35 0.4 0.45 1.5 2.0 2.5 3.0 3.5 -20 -10 0 10 20 -45.0 -22.5 0.0 22.5 45.0

0.2-0.5 GHz Flux Density (mJy) 1-4 Flux Density (mJy) Figure 8e. Dynamic spectra of the 4-hour observation of AD Leo on 2015 July 19, in the style of Figure 8a. In this epoch, we identify two coherent bursts: long-duration emission at 1-1.6 GHz throughout the observation, similar to the event on 2015 July 4 (Figure 8d), and two short-duration events that may be related, both at t∼140 min: a 1.6-2.2 GHz right-polarized burst lasting 30 sec, and a 2.8-4 GHz burst lasting 6 min. COHERENT RADIO BURSTSON MDWARFS 41

Frequency (GHz) 0.25 0.35 0.45 0.3 0.4 1.5 2.0 2.5 3.0 3.5 0.0 0.0 60.0 60.0 Stokes I, 0.2-0.5 GHz Stokes I, 1-4 GHz 120.0 120.0 Time (min) since 2015-09-05 20:24:24 UT 180.0 180.0 AD Leo - 2015-09-05 0.0 0.0 0.0 60.0 60.0 60.0 Stokes U', 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz Stokes V, 1-4 GHz 120.0 120.0 120.0 180.0 180.0 180.0 0.25 0.3 0.35 0.4 0.45 0.25 0.3 0.35 0.4 0.45 1.5 2.0 2.5 3.0 3.5 -25 0 25 -10 -5 0 5 10

0.2-0.5 GHz Flux Density (mJy) 1-4 Flux Density (mJy) Figure 8f. Dynamic spectra of the 4-hour observation of AD Leo on 2015 September 5, in the style of Figure 8a. In this epoch, we identify two coherent bursts: long-duration broadband emission at 1-2.5 GHz, lasting >1.5 hours, and a strongly-polarized short-duration event at 0.29-0.36 GHz at t∼190 min. 42 VILLADSENETAL.

UV Cet - 2013-05-26 Stokes I Stokes V 45

30 5.5 5.5

15 5.0 5.0

4.5 4.5

4.0 4.0

3.5 3.5 0 Flux Density (mJy)

Frequency (GHz) 3.0 3.0

2.5 2.5

2.0 2.0

-15

1.5 1.5 -30

-45 0.0 30.0 60.0 90.0 0.0 30.0 60.0 90.0 Time (min) since 2013-05-26 17:35:49 UT

Figure 8g. Dynamic spectra of the 2-hour observation of UV Cet on 2013 May 26, in the style of Figure 8a, but covering 1-6 GHz. This epoch is shown using matplotlib’s “symlog” scale (linear near the origin, logarithmic at large flux densities) in order to highlight events at a range of intensities. This epoch contained a short-duration event (two right-polarized sub-features at t∼30 min, together spanning at least 1-6 GHz), and a long-duration event (1-6 GHz, last 25 minutes of observation). COHERENT RADIO BURSTSON MDWARFS 43

Frequency (GHz) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 0.0 30.0 Time (min) since 2013-06-02 17:28:13 UT Stokes I 60.0 UV Cet - 2013-06-02 90.0 0.0 30.0 Stokes V 60.0 90.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 -15.0 -7.5 0.0 7.5 15.0

Frequency (GHz)

1.5 2.0 2.5 3.0 Flux Density3.5 4.0 (mJy) 4.5 5.0 5.5 0.0 30.0 Time (min) since 2013-06-02 17:30:13 UT Stokes I 60.0 UV Cet - 2013-06-02 90.0 0.0 30.0 Stokes V 60.0 90.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 -6.7 -3.3 0.0 3.3 6.7

Flux Density (mJy) Figure 8h. Dynamic spectra of the 2-hour observation of UV Cet on 2013 June 2, in the style of Figure 8a, shown twice with different binning and color scales. There is a long-duration event spanning 1-4 GHz and lasting roughly 1 hour, with multiple bright short-duration features embedded within it. 44 VILLADSENETAL. UV Cet - 2015-05-15 Stokes I Stokes V

17.5

1.5 1.5 0.0

-17.5 Frequency (GHz)

0.0 30.0 60.0 90.0 0.0 30.0 60.0 90.0 Flux Density (mJy) Time (min) since 2015-05-15 16:56:10 UT Figure 8i. Dynamic spectra of the 2-hour observation of UV Cet on 2015 May 15, in the style of Figure 8a. Only 1-2 GHz was observed on this date. There is a short-duration burst spanning 1.2-2 GHz at t∼60 min. COHERENT RADIO BURSTSON MDWARFS 45

UV Cet - 2015-05-16 Stokes I, 1-4 GHz Stokes V, 1-4 GHz 80

3.5 3.5

40

3.0 3.0

2.5 2.5 0

2.0 2.0 1-4 Flux Density (mJy) -40

1.5 1.5

-80 0.0 30.0 60.0 90.0 0.0 30.0 60.0 90.0

Frequency (GHz) Stokes I, 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 50 0.45 0.45 0.4 0.4 0.35 0.35 25 0.3 0.3 0.25 0.25 0.0 30.0 60.0 90.00.0 30.0 60.0 90.0 0 Stokes U', 0.2-0.5 GHz 0.45 0.4 -25 0.35 0.3

0.25 0.2-0.5 GHz Flux Density (mJy) -50 0.0 30.0 60.0 90.0 Time (min) since 2015-05-16 16:28:04 UT

Figure 8j. Dynamic spectra of the 2-hour observation of UV Cet on 2015 May 16, in the style of Figure 8a. There is a coherent burst in the last 20 minutes apparently spanning the entire observed frequency band (at least 0.3-3.7 GHz). We classify this event as “long-duration” due to its morphological similarity to the start of other long-duration events on UV Cet. 46 VILLADSENETAL.

Frequency (GHz) 0.25 0.35 0.45 0.3 0.4 1.5 2.0 2.5 3.0 3.5 0.0 0.0 60.0 60.0 Stokes I, 0.2-0.5 GHz Stokes I, 1-4 GHz 120.0 120.0 Time (min) since 2015-07-04 12:18:18 UT 180.0 180.0 UV Cet - 2015-07-04 0.0 0.0 0.0 60.0 60.0 60.0 Stokes U', 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz Stokes V, 1-4 GHz 120.0 120.0 120.0 180.0 180.0 180.0 0.25 0.3 0.35 0.4 0.45 0.25 0.3 0.35 0.4 0.45 1.5 2.0 2.5 3.0 3.5 -50 -25 0 25 50 -110 -55 0 55 110

0.2-0.5 GHz Flux Density (mJy) 1-4 Flux Density (mJy) Figure 8k. Dynamic spectra of the 4-hour observation of UV Cet on 2015 July 4, in the style of Figure 8a. This epoch contains a 90-minute-long burst spanning at least 0.3-4 GHz (also detected at 8.2-8.5 GHz in simultaneous VLBA observations, publication forthcoming). COHERENT RADIO BURSTSON MDWARFS 47

Frequency (GHz) 0.25 0.35 0.45 0.3 0.4 1.5 2.0 2.5 3.0 3.5 0.0 0.0 60.0 60.0 Stokes I, 0.2-0.5 GHz Stokes I, 1-4 GHz 120.0 120.0 Time (min) since 2015-07-18 11:23:15 UT 180.0 180.0 UV Cet - 2015-07-18 0.0 0.0 0.0 60.0 60.0 60.0 Stokes U', 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz Stokes V, 1-4 GHz 120.0 120.0 120.0 180.0 180.0 180.0 0.25 0.3 0.35 0.4 0.45 0.25 0.3 0.35 0.4 0.45 1.5 2.0 2.5 3.0 3.5 -50 -25 0 25 50 -100.0 -66.7 -33.3 -0.0 33.3 66.7 100.0

0.2-0.5 GHz Flux Density (mJy) 1-4 Flux Density (mJy) Figure 8l. Dynamic spectra of the 4-hour observation of UV Cet on 2015 July 18, in the style of Figure 8a. We categorize the bursts in this epoch as 3 events: a long-duration burst spanning 0.35-4 GHz in the last 30 minutes (also detected at 8.2-8.5 GHz in simultaneous VLBA observations), a short-duration event consisting of a series of at least 4 short bursts spanning at least 1-3.7 GHz, at t∼70-95 min, and a short- duration burst at 0.28-0.37 GHz, at t∼135 min. 48 VILLADSENETAL.

Frequency (GHz) 0.25 0.35 0.45 0.3 0.4 1.5 2.0 2.5 3.0 3.5 0.0 0.0 60.0 60.0 Stokes I, 0.2-0.5 GHz Stokes I, 1-4 GHz 120.0 120.0 Time (min) since 2015-09-06 06:07:06 UT 180.0 180.0 UV Cet - 2015-09-06 0.0 0.0 0.0 60.0 Stokes U', 0.2-0.5 GHz Stokes V', 0.2-0.5 GHz 60.0 60.0 Stokes V, 1-4 GHz 120.0 120.0 120.0 180.0 180.0 180.0 0.25 0.3 0.35 0.4 0.45 0.25 0.3 0.35 0.4 0.45 1.5 2.0 2.5 3.0 3.5 -40 -20 0 20 40 -60 0 60

0.2-0.5 GHz Flux Density (mJy) 1-4 Flux Density (mJy) Figure 8m. Dynamic spectra of the 4-hour observation of UV Cet on 2015 September 6, in the style of Figure 8a. This epoch contains one event, a long-duration burst spanning 0.25-4 GHz (also detected at 8.2-8.5 GHz in simultaneous VLBA observations).